Predictably and understandably, this film about one of the first known people to undergo a surgical sex change has been criticised for tweaking the historical record and, more sophisticatedly, for its heteronormative approach to a transgender story.
One reviewer slated it as "part of a trend of queer and trans films that are actually about straight people".
It's true that Vikander, who plays Gerda, the wife of the transgender title character, is a central figure and her Oscar nomination in the supporting actress category is more tactical than reflective of her dramatic significance.
But, like the accusation of historical licence, it also misses the point. Director Hooper played fast and loose with the facts in The King's Speech, too, and it would not have been the film it was if he had not.
This film, based on a novel, not a biography, is aimed at a mainstream arthouse audience; and it consciously construes the story of Einar Wegener/Lili Elbe, as an extraordinary love story, not a polemic on sexual politics.
Read that way, it is a triumphant success.
The Wegeners, scrubbed-up and gorgeous bohemians, are successful painters in Copenhagen in 1926: he is a landscape artist and theatre designer, she a more popular portraitist, specialising in dancers and nudes.
When one of Gerda's ballerina sitters lets her down, she asks Einar to don stockings, pretty ballet slippers and romantic tutu and the camera lingers on his dawning realisation sparked by the change of clothes.
It seems almost superfluous to praise Redmayne, given his incarnation of the steadily shrivelling Stephen Hawking in The Theory of Everything. He is sense and sensuality made manifest in this scene, and in most of what follows as he walks the rocky road to his appointment with a German surgeon (Koch).
It is miraculous to watch as he captures the heady blend of excitement and terrifying danger that infuses this existential challenge: his limpid eyes are always full of love for her, but they seem fixed on something beyond, too, that she cannot understand.
At first, his occasional transformations play like fun, a boundary-stretching piece of public art. But as Einar reinvents himself as Lili, Gerda's struggles to deal with her loss become an essential part of the story: "I need my husband," she tells Lili in one key scene. "Can you get him?" If the answer doesn't break your heart, it may be worth checking whether you have one.
Movie: The Danish Girl
Cast: Eddie Redmayne, Alicia Vikander, Ben Whishaw, Sebastian Koch, Amber Heard, Matthias Schoenaerts
Director: Tom Hooper
Running time: 120 mins
Rating: M (nudity, sex scenes)
Verdict: Brilliant performances sustain an extraordinary love story.