Well, define "mental illness". It's clearly a disorder, it's literally called gender dysphoria disorder in scientific terms, but that doesn't mean it's not like they just pretend like they feel super uncomfortable in their own body because of its gender. Imagine you, as a guy, had always been forced to wear dresses, and make up, and do all "girly" stuff, or in fact the other way around, you'd be getting crazy. To them, it feels like they have a female brain in a male body, or the other way around.

BTW, talk about being butthurt over what other people do that's none of your business, if somebody wants to make himself a new version of a movie that he likes, let him do it, what do you care? There isn't "one official Shakespearean play", except the ones he actually wrote.