The world is filled with examples of people from different backgrounds who got married and raised families together very successfully. So yes: inter-tribal, inter-religious, inter-racial, inter-whatever relationships do work. They, of course, also have their own unique challenges and the individuals involved have to compromise on culture and values that they might not have had to discuss if they married someone from a similar background. If you marry your girlfriend, you will have to create a new culture. And it will involve answering some questions. For example: How will dowry be paid? Which tradition will we follow as we name our children? Etcetera.
Upsetting the parents
In your case, you have to figure out if you are willing to upset your parents and marry this woman. I have found that human beings complain when they are faced with change or a scenario that stretches them out of their comfort zone. Just look at Nairobi and the decision to block some roundabouts to ease traffic. Many of us complained and whined. A few weeks later, we see the logic and traffic has eased greatly.
I am not saying that your parents are complaining for no reason.
In fact, I suggest that you ask them to tell you exactly what they are afraid of.
That their grandchildren might speak a different language? That their new daughter-in-law might not value their culture or adapt to it?
Figure out the concerns
Listen to them and figure out if their concerns are actually valid – as opposed to just a mild discomfort based on stereotypes they may hold about your girlfriend’s community. And then speak to her about it. She might have some very useful ideas on how to deal with the situation. It will also allow you to discuss the aspects of your respective cultures that matter to each you.
If you really believe she is a good person and the best match for you, then you might have to tell your parents to shut up and get over their prejudice. Also, keep in mind that nothing cures bias like a cute little grandchild.