Are there Jewish zombies?

No, of course not. Zombies are not real. What a silly, silly question.

But... if zombies were real, could there be Jewish zombies?

If we understand zombie mythology correctly, zombies are reanimated bodies without a soul. So, if you believe one's Judaism resides in one's soul, then no, even if someone once Jewish is reanimated after death, that zombie is not Jewish.

But could a zombie convert to Judaism? Is that even possible?

Again, it looks like the answer is no. To convert to Judaism, you need to study. You need... a brain. (Yes, we realize Tom Arnold converted. The exception that proves the rule.) And zombies, even with their hunger for cranial eating, obviously lack a brain themselves.

So no, no Jewish zombies.

Perhaps Sam Raimi can address that when he inevitably comes back to zombies after the next Spider-Man...