One of the sexiest women in America has the PC crowd in a swivet. Scarlett Johansson, you see, is shooting a Super Bowl ad for SodaStream.

Huh?

As it turns out, SodaStream, the Israel-based booming “make your own soda at home” firm, has a plant in the Jerusalem suburb of Maale Edumim — which is on the “wrong” side of the 1949 ceasefire line.

That “green line” lasted for all of 18 years, until the 1967 Six Day War, and every proposed map for Israeli-Palestinian agreement has Maale Edumim on the Israeli side — but Johansson’s critics don’t care.

The global blame-Israel lobby long ago elevated that line to an almost holy status of “border”; anything Israeli beyond it is really, really bad.

Including SodaStream.

Enter the Boycott, Divest and Sanction crowd. BDS, as it’s known, calls for shunning Israel for all of its perceived sins — and knows it gets its best results when it asks for boycotts of “settlements.”

So Johansson, by agreeing to be SodaStream’s “first global brand ambassador,” became a BDS boogie woman.

The talented actress, mind you, has hinted she may launch a political career. In addition to being named (again) as “Esquire’s Sexy Woman Alive,” she’s an Obama supporter and a perfectly kosher lefty (who, incidentally, was born Jewish).

But instead of answering BDS jeers, she simply said she loves the brand and has used it for years, and that SodaStream’s “commitment to a healthier body and a healthier planet is a perfect fit for me.”

She could also add that Soda­Stream’s plant in Maale Edumim, one of three in Israel, employs 1,100 workers — mostly West Bank Palestinians, under the same conditions and salaries as Jewish workers. A fourth plant, in southern Israel, will hire mostly Bedouin Arabs, now suffering from high unemployment.

In other words, SodaStream boasts many corporate values admired by the politically correct crowd. But not for Hollywood’s anti-Israelis.

Ever since Vanessa Redgrave famously dedicated her 1977 Oscar acceptance speech to the plight of Palestinians, many entertainers have made a point of singling out the Jewish state for rebuke while ignoring abuses anywhere else.

Stars like Elvis Costello, Annie Lennox and Stevie Wonder canceled shows in Israel. Pink Floyd’s Roger Waters has dedicated his recent life and concerts to bashing Israel, complete with anti-Semitic rants.

Emma Thompson and several other actors recently signed a letter opposing the participation of Israel’s national theater, Habimah, in a British Shakespeare festival (though they evidently have no problem with a Chinese company performing “Richard III.”)

It’s not all bad: Justin Timberlake, Justin Bieber and Neil Young will play Tel Aviv this summer. And Lady Gaga, Alicia Keys, Madonna and Bob Dylan have in the past ignored the BDS crowd. (Dylan’s 1983 “Neighborhood Bully” is a perfect sendoff to Israel’s phony critics.)

But consider: In the 1970s, many in Hollywood were rightly puzzled by Redgrave’s admiration for plane hijackers, some quietly wondering whether her outburst wasn’t informed by old-fashioned British anti-Semitism. Today, her take is gradually becoming mainstream in Tinseltown.

Yes, Hollywood was founded by Jews. But it also cherished some particularly odious anti-Semites like Walt Disney (whose Nazi sympathies were airbrushed from Tom Hanks’ recent biopic).

Anyway, the hard Hollywood left is happy to boycott anything having to do with the Jewish state — including Israeli theater companies that systematically bash their government’s policies.

Others are torn, saying they support Israel in principle, but oppose “occupation.” So they’ll boycott anything labeled “settlements.”

In Hollywood, where misguided radical chic hasn’t cost anyone a juicy movie part in half a century, ignoring the anti-Israel catcalls is no easy thing these days. Sticking by SodaStream in such an environment is admirable.

Scarlett Johansson, it turns out, is much more than a pretty face. Her casual dismissal of the BDS crowd is downright sexy.