There is something very levelling about seeing a major Hollywood star walking past Primark. And not just any Hollywood star but Scarlett Johansson, twice crowned Esquire's "Sexiest Woman Alive", three times Woody Allen muse, Bafta winner, noted beauty. Yet, there she is, in her latest film, in a pair of stonewashed jeans and a fake fur coat, walking down a busy shopping street in Glasgow and, well, blending in. She looks normal. Ordinary, even. Strip a star of their Hollywood get-up, remove them from their Bel Air mansions, and it turns out that they look just like the rest of us.

Only Johansson is different. Theoretically, this is because, in Under the Skin, a low-budget sci-fi indie adapted from a Michel Faber novel, we know she's an alien. In reality, it's because we know she's Scarlett Johansson. We watch her prowling the outskirts of Glasgow, the in-between lands of industrial parks and council estates, looking for fresh man meat, and there is an eerie sense of alien universes colliding. Scenes include Scarlett Johansson on a bus. Scarlett Johansson being given directions to Asda. And Scarlett Johansson sitting in front of an electric fire in a council house watching Tommy Cooper on TV.

It turns out that transplanting a major Hollywood celebrity to a down-at-heel, working-class Scotland is about as close as you can get to seeing an alien walk among us. Celebrities may not be an actual master race – yet – but there is something weirdly jarring about seeing someone familiar from a thousand red-carpet photographs, walking down an ordinary high street full of the ordinary faces of ordinary lives.

When I meet her, however, Johansson, 29, is back in full Hollywood mode. She's been installed in a fancy suite in New York's Waldorf Astoria and has shed the ugly jeans and cheap boots. She's in spiky heels and a silky top and is groomed and coiffed with eyelashes like a camel's and a river of shining blond hair that flows around her shoulders. She is surrounded by a small army of publicists and minders. She looks neither ordinary nor normal. (Nor, noticeably, pregnant, as various newspapers claimed last week.)

I've just seen her in action at a press conference where she'd gone off on a long riff about Jonathan Glazer, the British director of the film who she calls a "visionary" and a "genius". And when I meet her, she says what an easy and enjoyable film it is to talk about. "Because it brings up so many questions. One of the journalists that I was talking to today, we ended up talking about the relativity of time. Whereas, normally, it's like 'So, what do you find sexy in a guy?' Or, 'If you had a superpower, what would it be?'"

It's one reason, presumably, that she took the part, though I'm curious to know the details. There's only about three lines of dialogue in the entire film, so it can hardly have been the standout script. The main point of her character is that she doesn't actually have a character. She's an alien. She doesn't do emotion. And it was filmed in Scotland. In winter. And most of the film consists of her standing around in wet boots and a too-thin coat. Or stripping off her clothes in a derelict squat and luring men into a vat of black ectoplasm. (At one point, she appears naked. Johansson fans, of which there are many, most especially the male variety, have been lighting up message boards for months with discussion of this particular fact.)

So why, of all the scripts she must get sent, did she decide to do this one? "I heard Jonathan was making a film and originally it was a very different story. But I met him, and it was very clear that he was struggling to figure out what he was doing with it, and what had attracted him to it. It wasn't his passion project but there was something in the idea of having a character that was an alien that could give him the freedom to be completely observant without any judgment. I think we were both interested in that. I thought it would be incredibly challenging to play a character that's free of judgment, that has no relationship to any emotion I could relate to.

"And for me, at this point, I think it much more interesting for me to look at something and know that I can play it, but not know how, rather than to look at something and go, 'Ah, I can do that.' And then just do it."

She spent several years talking to Glazer – a director who made his name with the Guinness surfer ad and went on to direct Sexy Beast, with Ray Winstone, and Birth, with Nicole Kidman. She became "part of the creative process" and found herself committed to the project even though the story and script changed, and it turned out that the dialogue she speaks (in an English accent) she more or less had to make up as she went along.

There's no doubt that it was a bold decision. It's neither a blockbuster like Captain America, the second instalment of which is to be released shortly, and for which she wore a catsuit and was paid millions, and nor is Glazer a huge name. Critics have been divided. It is, depending on who you believe, either "an intoxicating marvel; strange and sublime" (Time Out), or a "laughably bad alien hitchhiker movie" (The Independent). The Guardian's Xan Brooks reported that at the premiere at the Venice film festival, there was uproar with "an even split of cheering and boos".

What was that like?

"It was very strange. It was the first time I had seen the film with an audience and the first time I saw the film finished. And I was on this huge mezzanine so I felt super-exposed.

"Then at the end, when the lights came up… there was this sound of people cheering and booing at the same time, but with equal gusto. I didn't know how to react to it. I think I was just… I wouldn't say disturbed but I was sort of shocked. I looked over at Jonathan and he was filled with glee. Absolutely thrilled. We left the theatre and I was like, 'That was so strange,' And Jonathan was like, 'That was the best reaction! That was the most amazing sound I've ever heard in my life.'"

I don't think I've ever seen reviews quite so extreme, I say.

"I would way rather not have middle ground. I would way rather fail in someone's eyes than be that sort of tepid… that's the worst. I remember going to see Eyes Wide Shut and I saw it like three times in the theatre and the first time I saw it, I hated it. I had a visceral reaction to it I hated it so much. And then I was like, I have to see that movie again, I hated it so much. And then I loved it. I think in some ways I hated the emotional experience, it's like a visceral reaction. There's passion behind it. I can't ever totally fault a film that I absolutely hate."

A remarkable aspect of Under the Skin is that a lot of the people who appear in it aren't actors. They're normal people – who happen to be walking down a road minding their own business when a pretty lady pulls up in a van alongside them and offers them a lift to Tesco and then a film crew clutching disclaimers leaps out of the back.

At what point did Glazer tell you: "Oh yes, by the way, Scarlett, we haven't really got any other actors. We're just going to cruise the streets and find them"? "That happened later on. And none of us knew how it was going to work. We toyed with lots of different things like prosthetics, teeth, all kinds of things that would change my face but only slightly, when in fact there was no need to do any of that."

As a metaphor for alien life, it turns out that the relationship between celebrities and non-celebrities is pretty apt. And you could read the entire film as a parable for the Hollywood star system and the power dynamics of celebrities and their audiences. Johansson's character is literally feeding off poor, stupid mortals like us; but she's also shut out from their – ie our – world, and the tables can turn in an instant. By the end of the film, the hunter has become the hunted.

It's a point that Glazer seems to be deliberately making. He's spoken about how he originally wanted to cast an unknown. But then "the idea landed to put a Hollywood star in disguise and drop them into the real world… the incongruity of Scarlett Johansson in Glasgow… you're already in alien territory."

But it seems a shame that Johansson's strategic break from her more commercial films was to play a character who, for all her alien characteristics, is pretty familiar from her more conventional roles: the voluptuous siren whom men find irresistible. Her, the wonderful, recently released Spike Jonze film which sees Joaquin Phoenix fall in love with a computer operating system played by Johansson, is a much fuller role despite the fact that Johansson never actually appears on screen. "She creates a complex full-bodied character without any body at all," said Variety's reviewer, Scott Foundas. And it seems to demonstrate that Johansson is a much better actor than she's often given credit for; directors have a habit, as here, of lingering on her face, her body, and failing to give her much of anything else at all.

Her breakout role was playing a version of this in Sofia Coppola's Lost in Translation where Bill Murray's washed-up actor character cashes in on his celebrity by making cheesy commercials and bonds with Johansson's ingenue; and she's played similar roles in Girl With a Pearl Earring, and notably, three different Woody Allen movies, Match Point, Scoop and Vicky Cristina Barcelona. Allen has gone on record about Johansson's abilities as an actress: how she is "sexually overwhelming"; how she has a "zaftig humidity"; and how he believed that she has the "acting ability to be not just a passing pinup girl but a genuinely meaningful actress". And Johansson has responded in kind by saying that she would be prepared to "sew the hems of his pants if he asked me to".

But last month Dylan Farrow, Allen's estranged daughter, published an open letter in which she accused him of abusing her and condemned the film industry's silence on the matter. In it, she pointed a finger at actors who have worked with Allen, including Johansson. It must have been a very uncomfortable experience being named in the letter, I say. How did you respond to it? "I think it's irresponsible to take a bunch of actors that will have a Google alert on and to suddenly throw their name into a situation that none of us could possibly knowingly comment on. That just feels irresponsible to me."

And what has she made about the backlash against Allen? "I'm unaware that there's been a backlash. I think he'll continue to know what he knows about the situation, and I'm sure the other people involved have their own experience with it. It's not like this is somebody that's been prosecuted and found guilty of something, and you can then go, 'I don't support this lifestyle or whatever.' I mean, it's all guesswork."

So, has it had an impact on her relationship or affection for him? "I don't know anything about it. It would be ridiculous for me to make any kind of assumption one way or the other. "

She's flustered, and since I've been given the wind-up signal by the publicist, I move on to an even more difficult subject. SodaStream. When I Google "Scarlett Johansson" the fizzy-drinks maker is the third predictive search suggestion in the list, after "Scarlett Johansson hot" – before even "Scarlett Johansson bum". A month ago, Johansson found herself caught up in a raging news story when it emerged Oxfam had written to her regarding her decision to become a brand ambassador for SodaStream. The company, it transpired, manufactures its products in a factory in a settlement on the West Bank, and while "Oxfam respects the independence of our ambassadors," it wrote, it also "believes that businesses that operate in settlements further the ongoing poverty and denial of rights of the Palestinian communities that we work to support".

Johansson responded by stepping down from her Oxfam role. From afar, it looked liked she'd received very poor advice; that someone who is paid good money to protect her interests hadn't done the necessary research before she'd accepted the role and that she'd unwittingly inserted herself into the world's most intractable geopolitical conflict. By the time Oxfam raised the issue, she was going to get flak if she did step down, flak if she didn't. Was the whole thing just a bit of a mistake?

But she shakes her head. "No, I stand behind that decision. I was aware of that particular factory before I signed it." Really? "Yes, and… it still doesn't seem like a problem. Until someone has a solution to the closing of that factory to leaving all those people destitute, that doesn't seem like the solution to the problem."

But the international community says that the settlements are illegal and shouldn't be there. "I think that's something that's very easily debatable. In that case, I was literally plunged into a conversation that's way grander and larger than this one particular issue. And there's no right side or wrong side leaning on this issue."

Except, there's a lot of unanimity, actually, I say, about the settlements on the West Bank. "I think in the UK there is," she says. "That's one thing I've realised… I'm coming into this as someone who sees that factory as a model for some sort of movement forward in a seemingly impossible situation."

Well, not just the UK. There's also the small matter of the UN security council, the UN general assembly, the International Committee of the Red Cross, the International Court of Justice… which all agree that they're in contravention of international law. Half of me admires Johansson for sticking to her guns – her mother is Jewish and she obviously has strong opinions about Israel and its policies. Half of me thinks she's hopelessly naive. Or, most likely, poorly advised. Of all the conflicts in all the world to plant yourself in the middle of…

"When I say a mistake," I say, "I mean partly because people saw you making a choice between Oxfam – a charity that is out to alleviate global poverty – and accepting a lot of money to advertise a product for a commercial company. For a lot of people, that's like making a choice between charity – good – and lots of money – greed."

"Sure I think that's the way you can look at it. But I also think for a non-governmental organisation to be supporting something that's supporting a political cause… there's something that feels not right about that to me. There's plenty of evidence that Oxfam does support and has funded a BDS [boycott, divest, sanctions] movement in the past. It's something that can't really be denied." When I contacted Oxfam, it denied this.

I don't get a chance to return to the subject of Under the Skin. The publicist ends the interview. But as a parable for celebrities' relations with us ordinary folk, the difference in our lives, and that tension between where the power truly lies – With them? With us? – it doesn't get more acute. There's even a masked man on a motorbike who goes around scooping up the bodies. I should know – one of them escorts me from the room.