LOS ANGELES — More than at any time in its history, Hollywood is under enormous pressure to find performers who match the racial and ethnic traits of characters.

Ridley Scott was harshly criticized for using non-Egyptian actors to play Egyptians in “Exodus.” The director Cameron Crowe faced an online mob for casting Emma Stone as an Asian-American woman in “Aloha.” (He ultimately apologized.) When Warner Bros. announced that Rooney Mara would play Tiger Lily in its forthcoming “Pan,” the studio was served with a petition headlined “Stop Casting White Actors to Play People of Color!”

But does it remain acceptable — at this Caitlyn Jenner and Laverne Cox moment — for non-transgender actors and actresses to play transgender characters?

Hollywood is about to find out. Two high-profile new films, each with Oscar aspirations, star performers who are not transgender in major transgender roles. On Saturday, “The Danish Girl,” with Eddie Redmayne in the title role, will have its world premiere at the Venice Film Festival. “About Ray,” starring Elle Fanning as a teenager in early gender transition, arrives next Saturday at the Toronto International Film Festival.