Just from what I've heard and read, and I'm not expecting any bonus points, Judaism was then, as now, open to converts. Apparently, most didn't fully convert, but followed Judaism's moral precepts. That is, they didn't get circumcised and they still allowed Gentiles into their homes, but didn't worship other gods, except perhaps Caeser. I'm guessing they still couldn't get into the inner courts of the temple.
But the Bible is generally reliable on historical grounds, so I wouldn't discount it as a source for such info.