My own limited experience bears this out. During college and grad school I dated two black girls and, later when I was in the Army, I dated a Commanche girl. In all cases, these were relationships that developed out of mutual interests and some natural attraction. In the first instance, during the summer her parents found out and forbade her from seeing me, in the case of the second black girl, she was confronted by a number of other black girls on campus and threatened by them. With the Commanche girl, I'd been seeing her in and around the small city where I was stationed for a couple of months, when she asked me come out to her place to pick her up (she lived with her parents). It was with some shock that I found the tribal police wouldn't even let me on the reservation, and that her father had forbidden her to see 'that white army officer'. He even made her quit her job in town to work out on the reservation.
It's very funny, I hear all the stories of white families reacting badly, ala Guess Who's Coming to Dinner, but what I've actually seen has been the opposite.