(I've lived in Texas for uhhhh five years now, in Austin.)
You have to understand that Texas is a big place. Like any big place, there is significant diversity. The stuff you've said is what the government likes to project, but isn't really representative of the population as a whole.
(Furthermore, this is confounded by certain issues playing out very differently in Texas than elsewhere: the left is more likely to like guns, for example.)
For example:
> * Personal liberty is highly valued.
This is what they say, but not what they do. The state is constantly passing laws that restrict the freedoms of individuals.
> Pro individual ownership of guns, as well as self-defense.
This one is complicated. Certainly more people are pro-ownership of guns, but that doesn't actually mean they have them. Texas has the most guns in the county, but adjusted for population, it's 37th in the nation.
> * Oil is a big part of the economy.
It surely is, especially historically, but Texas has also generated more green energy than other states for a long time. Solar is huge, wind as well.
> * Socially conservative overall, with exception of some enclaves of more liberal or progressive values.
You're right in a certain sense: if you look at a map, it's mostly red. But a lot of that land has basically nobody living there, and the "enclaves" are large cities.
It's tough to track political affiliation, but most reports show it to be very evenly split. "When will Texas turn blue?" is a question people have been asking for a long time, and the details of why it has not are complicated. But winning elections is different than sentiment, and the sentiment is at least very closely tied.
> * Large percentage of people identifying as Christian.
This is true; it's about 75%.
> * Centralized editorial influence over school textbooks, for not just Texas but the nation.
Not just textbooks, but see also the fights over vouchers and trying to privatize the school system.
> * Aggressive anti-abortion push.
This is true from the state, but that doesn't mean it's popular: a 2022 survey said that 78% of Texas voters think abortion should be allowed in some form, and only 15% think it should be completely outlawed.
> I'm interested in whether there are conventions over how conflicting values are reconciled
To be blunt about it, the current conservative movement in America isn't really interested in ideological consistency. They just don't see it as a problem.