Seems like this would be a tricky thing to do because the Census Bureau has changed how they do race over the years. From some rudimentary googling, it looks to me like the percent of Texan selecting "black" has increased very slightly since 1980. There's no doubt whatsoever though that the Hispanic increase has been much more substantial. Any data for Asians? Even Hank Hill in the little town of Arlen saw an Asian family move in during the time period you studied.
I didn't do Asians by themselves just because in 1980 and 1990 their populations were so small, but by 2000 they really started to make a presence in Fort Bend and Collin Counties.
I lumped Asians in my "other" category with mixed race and Native Americans since Texas in 1980 and 1990 had pretty small populations of these races. But by 2000 Asians and more than one race really started to grow.
I might have maps of Other Races, but my laptop recently crashed so I'm living out of a flashdrive haha.
Texas has two very small indian reservations (only state recognized though) in Maverick County and in Polk County and in the 1980 Census when "other" race in the state was relatively low, you can clearly see these two counties stand out with their relatively small Native American population.