People could not tolerate at all the things that aren't normal or common for them. The values, beliefs, eating habits, chronemics, proxemics, kinesics and all related to non verbal language.
If someone is in a relationship with another person who isn't from their culture, I think the most important thing is the communication and tolerance. As well, culture have an important role in the nexus we create, in a relationship the two parts have to take in account that culture imposes boundaries to human beings. Sometimes we don't agree at all with the aspects of the culture we belong and we have the right to be what we want to, and not the things that it imposes to us.
But Culture still represents some of who we are, because it molds our thinking and our perspective of life, how we see and perceive it.