Hope this doesn't come off as Transphobic...
I’m constantly afraid of being called Transphobic but here I go.. The whole concept behind Dr. Frank N. Furter is he’s a transvestite. That’s a man who still identifies as a man but likes to dress as a woman, it breaks conventional gender roles and expectations of conforming to what is “normal” for that gender. Now if it’s a woman dressed as a man that also works as a transvestite. But here we have a beautiful woman and she’s dressed like a woman. Why would that freak Janet out unless she knew her before her transition and can’t wrap her mind around transexuals? Transvestite / Transexual is not the same thing. And a woman dressed as a woman (even if she was born a man) is not a transvestite.
I don’t mind when women play male roles like Wao Yoka as Dracula or men who have played female roles but in the case of Dr. Frank N. Furter it’s hard to understand what Janet is reacting to if all she’s seeing is a beautiful woman (who is obviously a woman) singing about being a sweet transvestite. We, the viewers, know she’s transexual but Janet does not know that. As she is a post-op trans woman with all the feminine physical features wouldn’t it have made more sense to have her dress as a man to be “shocking” when singing Sweet Transvestite? She’s not exactly breaking gender norm expectations in her wardrobe here.
PS. Reeve Carney is an excellent singer so I gave him credit where it's due. I loved him in Spider-Man Turn off the Dark and Penny Dreadful (Though he didn’t sing in that).