Texas was only 14% African american which meant White Texans didnt swung as much to Thurmond because there wasnt a high black population to cause that defection of Dixiecrats.
A more interesting question is how North Carolina and Georgia avoided the huge shift to Thurmond considering Thurmond's home state was between these two states and they both had high african american populations as a percentage of the demographics at a time.
For Georgia its because the Democratic state party backed Truman. I'm pretty sure it's the same reason for North Carolina. You see in the states Thurmond won he was the nominee of the Democratic Party in the state.