Answering for Jews:

It's a bit difficult to say--the individual circumstances of someone's life can really affect how "difficult" it would be. Parental objection, how reliant they are on parents, etc. Depending on where exactly they were, it could've been difficult to stay in either a Jewish or a non-Jewish space, given the degree of segregation. I'm reminded of Groucho Marx's quip, when told he wasn't allowed to swim in the pool at a country club, asking whether his children (whose mother wasn't Jewish) could go in up to their waist. It's possible such a family would face isolation and be excluded from both the Jewish and the non-Jewish world, but I don't think that makes the marriage really difficult per se, just that it made it somewhat more difficult to navigate the complicated world of Jewish/gentile segregation in the early 1900s.

Intermarriage was fairly rare, though. In the early 1900s the rate was somewhere between 2 and 7%, which isn't nothing (so you could well have known someone who was intermarried), but is still pretty uncommon. That didn't really change until after the 60s, when parental objections to a potential marriage weren't seen as so important, social barriers between Jews and non-Jews had fallen, and a generation of Jews had grown up outside neighborhoods that were majority-Jewish. Also it was another generation or two for general assimilation into American culture to take hold.

My source is Jonathan Sarna's "American Judaism".