So like most of you I hope, my first thought on seeing this thread was, “That’s funny, I know they act like goyim and don’t follow the Torah and do the mitzvos like us, but of course they’re jewish.” However, recently, my wife who’s doing Daf HaSha’ah showed me a Tosfos in Qiddushin who quotes a gemara in Sotah that clearly holds they’re not. [The Tosfos itself was kinda interesting till I realized I might be a gayr] Those who follow the Rambam will of course throw this out with the baby but for the rest of us.
The Gemara (Sotah 37b [Of course I didn’t look it up] says that at Har Sinai the Bnei Yisrael Took on 603,550 covenants as guarantors for each other. Tosfos derives from this that they did not become guarantors for the Eirev Rav. The obvious next step is that they also did not become guarantors for the women. ???? ????? ??.