OK, but that’s a separate issue from whether we believe in literal demons.
But here is why it is not inconsistent: first, we don’t hold that mythologies are just man-made. The false mythologies can have a lot of truth in them. But they don’t have the full truth or may be mixed with error.
Second, if I ask who gave me an anonymous present, I can come up with several answers. Some will be wrong, but at least one of these answers could be correct.
Lastly, if demons are real, then it would not be the case that they are based on Jewish mythology, but rather that Jewish mythology would have some sort of description of them. They would exist independently of Jewish mythology.
There are arguments that have been made for the historicity of key Jewish and Christian claims–for instance, the argument for Mt Sinai and for the Resurrection of Jesus (if Christianity is true, so was Judaism; if Christianity can somehow be independently shown to be true apart from Judaism, it would then follow that Judaism is true).
It’s not just randomly picking and choosing a mythology.