I'm looking for good and/or early example(s) of a movie in which a male actor plays a female part (or vice versa), where the gender-switch isn't used to enact comedic or horror elements.
Robin Williams playing Mrs. Doubtfire wouldn't count for two reasons: it is used for comedic purposes, and he's actually playing a man who dresses up as an old woman, rather than playing an old woman.
Philip Friedman playing the Old Woman in Insidious (2010) wouldn't count either, because the gender switch is used to prop up the horror.
Jared Leto playing Rayon in Dallas Buyers Club (2013) wouldn't count either, as he is playing a transgender woman.
So I am essentially looking for a film in which a man plays a woman (or vice versa), and it is done earnestly and "seriously", without an attempt at making the audience laugh or scared with that extra bit of dramatic irony. In fact, if the audience is fooled into thinking they are the role they're playing's gender, even better. Also, the earlier the better, too, to avoid "list", it might be nice to find the one that broke that ground.
A good example is Tilda Swinton playing David Bowie in a biopic, but it turned out to be only a rumor, so it can't be used as an answer.