Islamists also believe women's place is in the kitchen, so you can't be against both women and Islam.

How do you parse that? Say a rapist rapes women because he hates them. Say for the sake of argument I hate women too. Can I not be against both rapists and women? Or, what if that rapist also did other things, like terrorism. Do I have to support him because he hates women? It makes no sense.

You can't be anti-government and anti-semitic, because all anti-semitic ideologies are advocating a central government that controls everything.

Again, how do you figure? There are plenty of anarchist-adjacent people who also dislike the Jews. Anti-Semitism is not a government policy; you can hate the Jews and be fore an authoritiarian government, but you could just as easily think government should be abolished. Heck, one of the big complaints a lot of those people have is that the Jews run everything. If you don't like the Jews, and think they control government, abolishing the government seems a pretty good idea.