Except for the anti-Semites, who make up a decent chunk of his active base. Or are they also pro-Israel?

Yes.

Antisemite support of Israel is very common, because antisemites:

1. Have a lot of overlap with fundies, who believe that Israel MUST exist for the apocalypse to occur
2. Enjoy the thought of an ethnostate where they can deport all the Jews to
3. Hate Muslims more than Jews