it may be a problem to you but it is not a problem to Jewish leaders. They used to tell everyone that the Jews were just a religious group that could cause no harm. And whoever believed this lie was doomed to suffer later for it.

You bring up a point. That Jews are jews by their blood and not religion. They are a people before a religion. Religion is their shield against their enemies. But they remain forever a mixed Jewish race.

a Jew and a Judaist?

true... but what is the solution?

I don't see a way to present a new name to one of the groups...