My brother is happily married to a woman of another race and they have no problems. Her parents seemed reluctant to accept him at first- likely worried that he and his family would not have the same cultural values- but after meeting all of us they seem to have decided that we all came out all right and their daughter was in good hands, lol.
Come to think of it though, he did mention that when they were in the Carolinas recently, when they went out for meals they got ignored by waitstaff and stared at by other customers... people are so fucking shallow and rude.