Yes true but you can't live among the Greeks and Italians and not pick up a few converts to Judaism. The local synagogue in a small town is dying, some shekels pass hands and all of a sudden the rules are slightly bent. Or the man makes a good marriage financially and the man does not mind the pain of adult circumcision.
If the Ashkenazis picked up Steppe via the Poles or Ukrainians would not the same strict rules against mixed marriages hold?
First of all, your comment is insulting and borders on being anti-Semitic. Moreover, if you were familiar with the history of these periods you'd know that it wasn't the Rabbi you really had to worry about; he'd just excommunicate any member of his community who converted to Christianity. The problem was the priest or the Bishop if a Christian tried to convert to Judaism. They'd burn you at the stake.
That's over and above the fact that circumcision as an adult male was not a minor thing in the days before antibiotics etc.
Second of all, anyone marrying into the Jewish community even from the days of Constantine would have to willingly decide to become part of a despised and mistreated minority. By the Middle Ages, Jews had to wear distinctive symbols, only follow certain professions, live in certain circumscribed areas. At a certain point, the law demanded that they be locked into their ghettos at night in some areas, including Piemonte in Italy. At any time some aristocrat who didn't feel like paying back the loans he took out, or the merchants who couldn't take the competition, could whip up the mob, and the Jews would have to leave in the best case scenario, or face conversion or death in the worst case scenario.
It doesn't sound to me like a lot of men would decide it was worth it, even if they managed to meet a young Jewish woman, and especially if they were facing death if discovered.
However, we don't have to rely on common sense or what we THINK men would do. Let's try a novel approach. Let's look at the yDna of Ashkenazi Jews. "European" y dna is a "very" small percentage of the whole.
I hate to think, much less speak of it, but some of the what there is undoubtedly came as a result of the rapes reported during pogroms etc., although I'm sure many fetuses were aborted. There's a reason Eastern European Jewish women shaved their heads and wore head scarves.
So, the European genetic flow into Ashkenazi Jews was from European women, as papers showed starting 12 years ago by looking at mtDna.
It's also pretty likely that it took place before the time of Constantine, because from then on converting to Judaism was a crime punishable by death. You think a young woman could just disappear from a Christian home and appear in a Jewish one as a Jewish woman and no one would notice, like her parents, relatives, friends, people in the town? Even if some got away with it, you think that's enough to account for 40-50% of the Jewish genome?
The only other possibility for pushing it a bit forward in time would be if the women came from isolated areas in Christendom which were not yet completely Christianized. Priests were still coming up into my Lunigiana in the 500s to knock down the Statue Stelae which people still worshipped. Interestingly enough, one of the papers on the source of this female Gentile ancestry which flowed into the founding Ashkenazi population proposed that it was Italian women from Tuscany and further north who provided that ancestry to the Italian Jews who moved to the Rhineland. It's certainly true that some of the most esteemed Jewish families in the Rhineland came from that area.
As for the 10-15% Lithuanian/Polish ancestry in the Ashkenazim, from what I've read, at the time of their arrival in the east a certain percentage, particularly in Lithuania, were not yet Christians, so no priests or Bishops to worry about, and fleeing Jewish men were able to find mates among them.
When analyzing the past it's a very big mistake to impose on people in that past the lifestyles and attitudes of people today, especially Americans who no longer place any value on ethnicity and preserving that ethnicity. You have to look at people as they were.
A very good friend of mine is 100% descended from Germans who moved to the area of the former Yugoslavia early in the Middle Ages. For hundreds and hundreds of years these Catholic Germans lived surrounded by Orthodox Slavic speakers, but never admixed. They spoke German at home, went to German schools, and German Catholic churches, read German language newspapers, and married other Germans. Yet you believe large numbers of people crossed the line, risking their lives, to admix with Jews once the walls came down? It worked the other way round too. Good grief, the family of a friend of mine who married a gentile sat shiva for him. He was DEAD to them; literally.