Today, intermarriage is very high. A majority of American reform Jews marry people who are not Jewish, but this was obviously not the case historically. What can we infer about pre-modern intermarriage between European Jews and their gentile neighbors?
For three reasons I would expect such pairings to be almost unheard-of:
The historical malignation and segregation of Ashkenazi Jews would have given surrounding Christians little incentive or opportunity to marry into their communities.
The matrilineal nature of Jewish identity means that Jewish community leaders had a very big vested interest in ensuring that Jewish women married Jewish men, and vice versa.
The religious nature of marriage would have been an obstacle, as I assume many priests, preachers, and rabbis would be unwilling to marry couples of differing faiths.
However, genetic evidence suggests that substantial Northern European ancestry is almost universal among Ashkenazi Jews: http://m.livescience.com/40247-ashkenazi-jews-have-european-genes.html
Was this due to intermarriage in Roman Europe, before institutionalized antisemitism existed, or was intermarriage in Christian Europe actually somewhat common?
However, genetic evidence suggests that substantial Northern European ancestry is almost universal among Ashkenazi Jews: http://m.livescience.com/40247-ashkenazi-jews-have-european-genes.html
These things are not actually contradictory. Over very long timescales, even a small level of non-Jews and Jews having children and being Jews eventually adds up to a substantial level of admixture, so eventually the mixed-in genes can be found throughout the community. 1% of Jewish women being converts in every generation would eventually add up to a pretty substantial share of Jewish ancestry, over a timescale of thousands of years (which is how long there have been Jews in Europe). Note that half (40% of the total) lead back to a total of four women. All this evidence does not mean that 80% of marriages were intermarriages the same way 50% of American Jews today marry non-Jews. If 80% of marriages were intermarriages Jewish genetics would be European-dominated to an even greater extent.
Anyway, I think the issue here is that you're seeing medieval marriage's religious life in modern terms. I don't think the term "intermarriage" is accurate for what was probably happening at this point. It is entirely possible that there was a fair degree of conversion into Judaism at earlier times. There is (a very limited amount of evidence, but evidence nonetheless) that conversion to Judaism was not unheard of in the early medieval period. These would be women converting in, so not intermarriages, and a Rabbi would be happy to perform them in most cases. But even if they weren't, much of Europe was a bit of a Jewish "wild west" in the early medieval period. It's possible that Jewish men, especially ones who migrated to far-flung areas, would've just fudged things and married a non-Jewish woman--there'd be hardly anyone there to object, no real community leaders, no Rabbis, etc. While late medieval Jewish communities were often segregated, this was not always the case, and was usually not the case in the early medieval period. The prejudice against Jews we think of in the late medieval or early modern period was not so ingrained everywhere in the early medieval period, so it's definitely possible.
The religious nature of marriage would have been an obstacle, as I assume many priests, preachers, and rabbis would be unwilling to marry couples of differing faiths.
I'd like to tag in /u/vertexoflife here. In the medieval period marriage was usually regarded as a private affair, requiring no clergy (though I suspect I'm mischaracterizing it). Jewish marriage does not require Rabbinic involvement even today, though it's almost always used now. A Jewish man in a far-flung area not terribly educated in Jewish law or practice might be happy to marry a non-Jewish woman so long as she practiced Judaism from there on out, and never thought "gee I really ought to have a Rabbi do this". As for the other clergy, nowadays it's conceivable that an intermarried couple would be married by a clergy member from one religion but the child would end up another (to have genes in the modern Jewish community, the children would have to end up Jewish somehow). But in the past, where religion was more a way of public group-identification rather than privately held beliefs, one married couple practicing two religions would be quite unusual. But despite that it would've been possible for Jewish men to marry non-Jewish women and have their children end up Jewish.