I dated an Indian girl for about 6 years and I am essentially white (half scandanavian/half turkish). My family couldn't care less who I date, which is awesome having that kind of support, but her family was like a brick wall for 5 of those 6 years. Since I wasn't a "nice indian boy" trying to penetrate that wall took a metric shit-ton of effort and even then I was never fully accepted.
It was pretty horrible being shunned at gatherings and such but if you like the person you just gotta go for it and worry about yourself. At the end of the day its your life and even if they think it's bad and don't condone it, they'll love you for who you are and will hopefully come around eventually if they see that the person you're with is awesome.