Interesting question. I thought there was just one race on earth; The Human Race.
If you are actually talking about people from different cultures or countries, then of course, yes. Why is this even a question?
All humans are basically the same no matter their ethnicity or birth location. We all want to love and be loved, be safe, have a roof over our head and to eat.
I am English and married to a Thai. It is not always simple to when you date or marry someone from a vastly different cultural background but its very very rewarding as you learn more about each other and your respective cultures. I personally think everyone should marry someone from a different religion or culture as it would make the world a more understanding and peaceful place.
If you like someone, and they like them, then date them and respect their culture as they will respect yours. It's that simple.
Every happiness to you :-)