There's a big difference between being pro-state-of-Israel (Zionist), and being pro-jewish-people in general. They do not necessarily go hand in hand.

Fundamentalist christians are typically Zionist because the state of Israel is necessary for the second coming of christ. It's entirely self-serving, not a belief they hold because they like jewish people at all. So being zionist and also antisemitic is pretty common because people are racist assholes.