I think you're right about all this. Just wanted to add that this joke is (a little) funny because it simultaneously points out that trump and Elon are misogynistic and kind of gleefully watches them squirm about it, since you know they are also reading it in their own social media feeds.

If someone is offended by this joke, I would agree it's kind of hypersensitive but more importantly they are missing what the joke means at all. They noticed concepts they get upset about and not really understood how the concepts are being used.

Tldr; This joke is funny because it points out these assholes' bigotry and taunts them with it. It kind of trusts the audience to see that the entirety of the joke is inherently mocking someone for being a bigot.