I don't think there is any direct evidence of DKR bigotry. It's mostly inferred by those who disliked him.
The African American high schools in Texas had their own, segregated organization for competition until the late 60's. I believe it was called PVIL.
There were certainly intergrated schools before that. Warren McVay became a legend in San Antonio before going to UHouston.
But Royal's personal views had less impact on how Texas recruited, than the school's academic leadership. The same accusations were made against Bear Bryant. There was likely some justification for the accusation for both. But both would have preferred the best players they could recruit. But there were a multitude of other factors.
Maybe most important was the sad fact that black kids in Texas, for a variety of reasons, received inferior public educations in that time frame.
In Plano, integration at the high school level came in 1964. It's not a coincidence that the school's first state title came a year later. We had several high quality black athletes. The first to get a football scholarship went to OU, after a year at juco. He started his first game, didn't perform up to expectations, didn't play much after, and left school shortly after the 1968 season. Because of a poor elementary education, he never really caught up academically. That was a very common tale.
Prentiss Gautt jumped through a lot of hoops, starting without a football scholarship at OU. He was chosen by African American professionals in OKC for an academic ship to attempt to integrate OU's football program. Gautt was successful at both football and academics, because he was a very bright man.
Texas recruited Whittier because he was a quality student. Same with Jerry Levias earlier at SMU.
The inherent racism at UT in the 60's and before had a whole lot more to do with Texas not recruiting a black athlete until the late 60's. Accusations of racism get tossed around way too often. If you want to call Royal a racist, you ought to have specific evidence of a personal racist act, rather than your personal inferences based on the institutional racism of his employer.