Judaism was always an ethno-religious identity, that is very clear in the Old Testament. It is true that there were times when the borders of Judaism were less clear than today, for example in the Pre-Christian Roman Empire, when likely quite a few non-Jews converted. There is a very strong debate among historians about the level of conversion tough, apparently many Romans and Greeks became "God-fearers", they followed Jewish rites and traditions, and attended Synagogues, but did not strictly convert (no circumcision for example). The existence of that type of person is a proof of the ethnic character of Judaism in Ancient Times. It is just unimaginable the same happening in Christianity or Islam, those "God-fearers" would have converted if they started attending a Church or a Mosque.
The first Christians were undecided about the ethnic character of Christianity? To Saint Peter Christians should be Jews and follow Jewish laws, though "God-fearers" were also allowed. Saint Paul (who also was of Jewish origin), on the other hand claimed Christianity should be Universal: "There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus ". His side quickly won the theological debate, and Christianity separated from Judaism.