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...