“Our culture” (mostly western European) does not care if men play women (or vice-versa) in a play. If anything, like other have mentioned, in condones it. Stop acting like what you believe is the arbiter of culture. What you believe is nothing and meaningless, and a minority in our society.
Even if you were correct (which you absolutely are not), it wouldn’t matter because we don’t have to continue doing and believing the same things that were once believed. We can imagine and create a better world that let’s people be what they want and be happy. We don’t need you to agree to it, but it’d be better if you at least weren’t hostile to people trying to live their lives and not bothering you.