I read a book on the conversion of Europe a few years a go (I can’t think of the specific name at the moment) that revealed a lot of interesting things about the relationship between Christianity and Judaism in earlier Europe.
First of all, Europeans were converting to Judaism in significant numbers before the fourth century, especially in certain zones where non Romans were encountering significant Jewish communities of farmers, merchants and craftsmen. The Rhine valley would be one of those areas.
Also, there was considerable traffic either way from Judaism to Christianity and from Christianity to Judaism in many places from the first century up until the eigth century. There being an association in the minds of Europeans between the two that sometimes bordered on confusion (although I cannot imagine why). One mention specifically of a cathedral canon who converted to Judaism in sixth or seventh century Gaul that was notably upsetting at the time.
It seems it is likely that a high proportion of European Christians have some ancestry that passed through Judaism at some stage, even having ancestors who were Palestinian Jews who migrated west. Likewise there is likely some proportion of ancestry of European Jews (at least from western Europe), who had been Christians at some stage (perhaps for several generations), and another earlier proportion who had been European pagans.
Michael