Texas is a purple state, just like every other state. It's a light purple state, but not a light as Wyoming or Oklahoma. Voter suppression, gerrymandering, and the Electoral College keep it looking completely red, but it actually isn't. A lot of immigrants live there, and not just ones from Mexico. When I lived in Texas in the early 90s, the governor was Ann Richards, a Democrat. Sure, since then they've gotten idiots like Ted Cruz and Greg Abbot, but Beto O' Roarke only lost to Cruz in the last Senate race by 2% points.
A lot of the attitudes you've talked about as regards to rural Texans aren't wrong, but 4 of the biggest cities in America are in Texas. Austin is kind of the world capital of non-conformity. I don't know what the answer is for turning Texas to an even lighter purple, but I do think that things are lot more nuanced than they appear on the surface.