People who say "I believe in equality" and immediately follow that up "I mean, I'm a feminist"

And it makes it worse when people say after that "Feminazis aren't TRUE feminists." Because that's a logical fallacy. The no true Scotsman fallacy to be more precise.

Speaking of which, allow me to educate you on what the no true Scotsman fallacy is if you don't already know (in which case, you don't need to hear this so you can leave if you want to)
The no true Scotsman fallacy basically refers to changing the definition of something to exclude something else.

As an example I'll use the argument my mom made today, that being "Jehovah's Witnesses aren't TRUE Christians"
Now...
Let's look up what categorizes someone as a Christian-

And what do Jehovah's Witnesses do?

They spread the message of their interpretation of the Bible and believe that Jesus is God.

Therefore, they are Christians by definition.

That doesn't mean it's not a cult though.
It's definitely a cult.
It also doesn't mean that all denominations of Christianity are as bad as Jehovah's Witnesses.
That also isn't true.