To be considered a Jew, a person had to follow the laws of the Torah, and the males had to become circumcised.
Josephus described the different priestly classes. They had differing views on salvation, heaven, hell, etc because those issues were never addressed by Moses in the Torah. He left it an open-ended question!
When the Jerusalem Christian leadership strictly adhered to the precept that all Christians should be Jews first, they basically were saying that all male converts had to undergo circumcision.
That drastically cut down on the number of potential converts for obvious reasons!
Paul, who was half-Greek, saw this as a de facto way to keep the gentiles out of the movement, though throughout history Jewish conversion always required circumcision.
Peter also freely associated with Gentiles, though he (apparently) was a full-blooded Jew. We know little about his activities as he likely could not write. Paul, trained as a Second Temple priest, wrote extensively and many of those writings survive, so his perspective on Christianity dominates.
Flavius Josephus was also a trained Second Temple priest. Read him to learn what it entailed to be Jewish in the early first century A.D.
source Hagan “Year of the Passover”, “Fires of Rome”