The Texas GOP was still developing in the emerging suburbs of the state. Texans were still willing to vote for Jimmy Carter in 1976 (Southern evangelical Christian Democrat). It helped Carter that Ford was a moderate Northern Republican.
It was not until 1980 that Texas really became a firmly Republican state. Both Reagan and Bush Sr. contributed to this development. However, it should be noted that some of the rural counties in Texas and other Southern states that voted for Wallace, also voted for Carter in both 1976 and 1980. It was the suburbs of Southern cities that provided the base of support for the GOP to emerge as the dominant party in the South.
Texas also was a solid Democratic state at the non-Presidential level until 1994. I actually wouldn't say it could be confirmed as a solid Republican state for President until 1992 when they didn't vote for Clinton.
