outhouse
Atheistically
They wouldn't be Jewish if they didn't convert, they would have known what "Judaism" means.
Then that is not converting to Judaism, there is a difference.
No, they would have viewed themselves as non-Jews practicing a faith similar to Judaism.
No, "Jews" up until recently were only considered such if they were ethnic Jews or straight converts, not Christians or any other non-Jews practicing a faith similar to Judaism. 'Judaism' as I've stated before is reliant on the Torah laws to distinguish itself from other sects of Abrahamic religions.
Your missing the point.
these Hellenistic people were worshipping Judaism for generations. They knew the religion as well and understood it as any other Jew does. Some of these people did convert fully to Judaism, but the majority of these people did not, and that is exactly who Paul took his message too.
If your father had worshipped the monotheistic god under Judaism, and you did all your life born into it, and you taught your children Judaism, you would think you were Jewish as you were a follower of Judaism and it was all you had known.
Again one more time, Judaism before the temple fell was wide and diverse and open. There were almost as many beliefs as there is imagination for such. All based on geographic location more then anything else. Typical Judaism in one place was much different then others during this period. Saducees had is so perverted it didnt even ressemble typical Judaism nor the beliefs they followed, but viewed thmeselves as Jews. You had sects like John teaching one way, Jesus teaching his way, and a thousand others all teaching their own version.
Wide diversity with different levels of adherance to the Noahide laws, so when some Hellenistic people wanted to worship the same way, they could and did.
the names they were called all had to do with who was calling said name or phrase