I'm not Jewish. But I live in an area where there lots of Jewish people, and I have Jewish friends. Most of them have curly hair of some degree, and nearly all straighten their hair. That's not so different from curlies of other origins, who also mostly straighten. Maybe it's as much to be in fashion as to not look Jewish, I don't know.
I'm not in an Orthodox area, but the Orthodox women wear wigs, right? So I guess they can have any kind of hair they want.