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.
North Carolina was because there was a large population of Mountain Republicans in the west descended from communities that opposed secession, so that having the state party back Thurmond would have most likely handed the electoral votes to Dewey. Georgia was because the “Three Governors Crisis” led Hermann Talmadge to fear a challenge in the concurrent gubernatorial race if he backed Thurmond.
in Texas, as others have pointed out, there was not the Republican threat found in North Carolina (or in Tennessee, Oklahoma, or Virginia) but there were relatively fewer Negroes and consequently more concern over economic issues – which even among an electorate limited by poll taxes to a quarter of those eligible favoured Truman over Thurmond very strongly.
