Since I live in a multicultural country, I've pretty much had friends from different cultures all of my life. When I was younger there weren't any cultural clashes, we just respected each other and got along just fine. We rarely discussed cultural differences since we didn't think it was that important- we were friends and that was all that mattered. This may also be due to the fact that those friends had been living where I live for a long time or were also born here, so I guess they were also influenced by my culture. When I studied abroad is when I truly met people from different cultures, some I went along with really fine, and some clashed. In one class I was put together with people from the USA, Australia, Canada, South-Korea, Taiwan, France, Spain and Italy. I've read about some cultures I'm interested in, and I feel comfortable in those cultures. Making friends with people from those cultures was no problem- as I understood those cultures for as far as I possibly could for an outsider of those cultures. However, there were some misunderstandings with people from the South European countries, haha! (I'm North European)
I dated outside of my culture once, and went out with a Moroccan guy. I can't say much about that since we only went out for a short time, and he lived here all his life. I do remember him saying once that his mom wasn't all too keen on European girls because of their different morals and values. Despite the fact that he was far more respectful than my previous exes I didn't really notice that many cultural differences. Again, we went out for only a short time so who knows the differences would've showed after a while. But it really clicked with him- there was this instantaneous friendship and liking we had for each other.
I don't think a different culture should be a deal-breaker for relationships as long as both persons are willing to (try to) understand the other person's culture. I think it's important to be open towards other cultures, you could learn a lot and gain different insights!