Rejoice! The new Ghostbusters is good. Very good, in fact. It had to be. No comedy has faced more advance scrutiny - even hostility – than Paul Feig’s reboot of Ivan Reitman’s beloved 1980s hit.

It didn’t seem to matter Feig’s track record with mainstream comedy is peerless. Since hitting his big screen stride with Bridesmaids (2011), the sitcom veteran has consistently delivered: his two subsequent two female-led comedies, The Heat (2013) and Spy (2015), were spry and hilarious; both fronted by his muse, the venerable Melissa McCarthy, who he corralled into this Ghostbusters re-imagining. If ever there was a duo to bring the series into the 21st century, surely this was it.

Yet for many – chiefly blowhard middle-aged fanboys – their names spelled the apocalypse and the whole project was damned. The memory of their childhood favourite was being destroyed, they argued, by some hare-brained revisionism. A campaign was mounted – successfully – to make the first trailer for the film the most disliked in YouTube history.

Such backlash was notably absent when Planet of the Apes was revamped by Tim Burton, then again by Rupert Wyatt. Likewise when Fede Alvarez dared to reimagine Evil Dead for a new generation. For what incensed Ghostbusters fanatics, it seemed, was Feig’s idea to reverse the genders of the ghostbusting quartet – a decision whose politics his film tackles bluntly and frequently, without sacrificing laughs for sermonising.

The nods are pointed, and there’s no doubting who’s in the cross-hairs. Our main villain, a sad-looking loner on a mission to “cleanse the world” by letting ghosts loose on Manhattan via a device that amplifies paranormal activity, lambasts the heroines for shooting “like girls”. Our first major laugh involves a specifically female anatomical issue. In one remarkably on-the-button scene, McCarthy’s character takes offence to a comment left under a YouTube video of the women facing off against an especially angry demon. It reads: “Ain’t no bitches gonna hunt no ghosts.” It’s almost inevitable that, in the climatic brawl, the quartet aim their plasma blasters squarely at a giant male ghost’s crotch.

The fanboys are right: we are a long way from Reitman’s original. How far is worth highlighting: after all, that first film opened with a strikingly pervy Bill Murray conning his way into a late-night date with a young female pupil. The second gave Sigourney Weaver nothing at all to do but worry about her baby’s safety.

But as well as that spirit of rebellion and defiance, there’s also warm-hearted nostalgia coursing through this comedy’s veins. Murray and Weaver, along with other first film favourites such as Dan Aykroyd, Annie Potts and Ernie Hudson all make appearances, with Murray getting the most screen-time as a paranormal debunker. The late Harold Ramis also gets a touching, albeit fleeting, tribute.

Yet though hats are respectfully doffed, this is a four-woman show, deftly managed to allow all the leads – McCarthy, Kristen Wiig, Kate McKinnon and Leslie Jones – a chance to showcase their own distinct brands of comedy.

McCarthy is the “everywoman” of the picture, effortlessly grounding some far-flung proceedings as a bespectacled scientist. Feig grants her multiple opportunities to fling her body about with abandon (in particular when possessed by a grisly spirit), capitalising on the actor’s brilliant touch with slapstick. Wiig begins drolly mannered as an uptight professor, then loosens up a treat once the spooks start multiplying.

Since that first trailer, some scepticism had been levelled at Leslie Jones’s character: a no-nonsense subway worker whose street smarts prove an asset to the team. As well as a sexist backlash, Feig and co had to contend with accusations of gross racial stereotyping; not only did Jones’s character appear the sassiest, she was also the only non-physicist. Yet so supremely appealing is Jones’s performance – essentially a big-screen debut for the Saturday Night Live star – such considerations are steamrollered into oblivion. She’s simply hilarious.

Yet of the ensemble, it’s fellow SNL-alumna Kate McKinnon who proves the most compulsively watchable. Playing a brainy yet bizarre engineer in charge of perfecting the ghost-trapping machinery, McKinnon marshals a bevy of endearing quirks into a star-making, supremely confident turn.

As braindead yet puppyish receptionist Kevin, Thor hunk Chris Hemsworth acquits himself admirably, nailing misapprehension after misapprehension with lucid conviction.

Feig falls down a little in the final Times Square spectacular. This is his first effects-laden enterprise and he sometime ladles on the CGI a little thick. Such huge-scale action should never risk overshadowing the tremendous chemistry of the four leads. That said, he mostly orchestrates the chaos commendably, with rambunctious use of 3D; the ghoulish critters sometimes spill out of the widescreen frame, or spring right at you.

Most crucially, the mean-spirited reception to the film before anyone had seen it does not seem to have put a dampener on the movie itself. Fun oozes from almost every frame; likewise the energy of a team excited to be revolutionising the blockbuster landscape. Let’s just hope everyone will enjoy the view.

• Ghostbusters opens in the UK on 11 July, in Australia on 14 July and in the US on 15 July