It’s rare nowadays when a film suffers from a surfeit of tastefulness, but that’s the undoing of Tom Hooper’s “The Danish Girl.” Beautifully appointed and boasting an excellent cast, the semi-biographical film about Einar Wegener/Lili Elbe (1882-1931), one of the first persons to undergo sex reassignment surgery, is so cautious in dealing with the subject matter, so anxious to avoid the slightest hint of sensationalism, that it ends up exceedingly attractive to look at but curiously bland dramatically. One comes out of the glossy, ever-so-delicate film with the suspicion that the makers have gone entirely too far in seeking to avoid offending anyone in a mainstream audience.

Eddie Redmayne, whose expertise at transformation won him an Oscar playing Stephen Hawking in “The Theory of Everything, “gives a similarly impressive exhibition of technique here. He first appears as Einar, a successful painter of landscapes in late 1920s Copenhagen, apparently happily married to Gerda (Alicia Vikander), a much less successful painter of portraits. When Gerda needs a stand-in for her absent model, ballet star Ulla (Amber Heard), Einar agree to play dress-up, and the experience releases in him what has always been true—the fact that his maleness is a physiological mistake, and that beneath it Wegener is truly female. He begins dressing as an alter-ego called Lili, even going out posing as Einar’s cousin of that name, and looking so lovely in that guise as to attract the attention of a suitor named Henrik (Ben Whishaw).

Einar’s—and Gerda’s—escalating distress over the difficulty of balancing the two personalities and coming to terms with the increasing dominance of Lili leads Einar to seek medical treatment. Only after getting no help from traditional practitioners with sternly moralistic outlooks does he find Dr. Warnekros (Sebastian Koch), a decidedly non-judgmental German surgeon who’s willing to undertake the experimental but dangerous surgery to correct nature’s mistake. Throughout Gerda is supportive, as is Einar’s childhood friend Hans (Matthias Schoenaerts), now a Paris art dealer; but as Lili emerges in full, Gerda and Hans grow closer.

One can spend a good deal of time analyzing how Lucinda Cox’s script, adapted from David Ebershoff’s novel, diverges from the historical facts of Wegener-Elbe’s life. There are elements that are altered, some of them rather substantially. But as one must so often emphasize, docudrama is not the same thing as documentary, and Cox and Hooper have understandably excised elements that would complicate the narrative they’ve elected to tell—one that, in cinematic terms, places “The Danish Girl” in much the same place in the transgender genre that “Philadelphia,” for instance, occupied in dealing with homosexuality and AIDS back in 1993. It’s a prestige production designed to bring to a large audience a treatment of a topic many might feel uneasy with in a form that will elicit sympathy rather than discomfort.

The problem with that is that by avoiding any trace of edginess Hooper and his colleagues have reduced the life of a person revered as a pioneer in a movement that’s only now achieving unbiased status in contemporary culture to something so decorous that it possesses little emotional resonance at all. Hooper’s approach is so staid as to be enervating—even a nasty encounter Einar has with a couple of thugs in a park comes across as barely a tussle. And the sheer elegance of the production—designed by Eve Stewart, with art direction supervised by Grant Armstrong and gorgeous costumes by Paco Delgado, all shot in luminous images by Danny Cohen—adds to a magazine-feature feel. Even the score by the usually inventive Alexandre Desplat goes overboard, like too much whipped cream added to an already rich desert.

Redmayne is the final, and perhaps most debilitating, element. His performance is so studied, so carefully thought-out in its effects, that it leaves no room for spontaneity; despite the enchanting smile he can flash so disarmingly, neither his Einar nor his Lili seems real, and so one comes away admiring his work in terms of its proficiency as an acting exercise rather than as a portrait of a actual human being. By contrast Vikander does convey the ambiguities inherent in Gerda (even if the character doesn’t have the nuances of the real person). The rest of the cast do what is required of them as Hooper moves them around like well-made-up exhibits in a wax museum.

The story of Lili Elbe naturally demands sensitivity in the telling. But “The Danish Girl” takes that prescription entirely too far.