I would argue that the major reason for this is the Civil Rights Movement of the 1960s. During and after that time, racism has come to be socially unacceptable among the vast majority of Americans. Because of this, it is also much less acceptable to show any resistance to the idea of interracial relationships. (Of course, it also matters that so many of the people whose ideas were formed before that time period are now dead.)
A second, and related, cause is the fact that there have been so many interracial relationships in the time since the '60s that they no longer seem strange or unnatural to most people. As we see more and more interracial couples, we get used to them and they no longer seem as odd as they once did.
Finally, it may also matter that the US is becoming more and more diverse. More American young people are going to school with people of different races. This makes people of other races seem a lot more "normal" to them and they do not think it is strange to enter into romantic relationships with such people.