I've never heard of the gay comparisons, and that's a bit ridiculous. Especially since gays (men at least) are losing their oppression cred because, despite being gay, they're still "cis scum with p**ises".
As for comparing liberals/leftists to nazis, I've heard that occasionally too, and the way they're going, it's not really that hard to imagine. A group of people pretending to be a leftist-socialist group vilifying another group as the cause of all problems (white males = jews), trying to dictate what people can and cannot say or do, and trying to take away private weapons so the people can't fight back when they fully take power.