Yes, especially race/ethnicity. Usually the couple that in love able to accept that difference but the rejection will come from their family members(parents). And if the couple cannot convince their parents, break up will be the choice.
Difference has - I'm sure - been a factor in so many breakups. Not that I've ever been involved in, though. But if each person has a strong opinion towards it which goes against the other's, yeah, it could be a factor.