Not to try and violate any "politics" rules, but in general for your info that larger cities - Dallas, Fort Worth, Houston, Austin, San Antonio, El Paso will be your "bluer" areas. This trend mirrors other larger population center trends in other states and doesn't necessarily involve people coming from CA or other places. It just is. South Texas has always hosted a significant Hispanic population and that has been growing for many years. Counties outside of those areas - maybe the larger ones a couple of counties outside - will be your more "red" leaning areas. All the demographic/voting data and maps for the entire state is readily found online.
Note that in west Texas is not uncommon to have less than 4000 people in 1000 sq/miles. For the privilege of not having anyone anywhere close to your lawn LOL you will be driving. As an example of more rural west Texas, I live in Taylor County, city of Merkel. About 2600 people. Decent town more or less. We're 20 miles west of Abilene, which has a population of around 120,000. In 1960, it was around 100,000, so growth is very slow, ebbs and flows. With that info, consider that Merkel is the 2nd largest town in Taylor County. The county coves 919 sq/miles and had a TOTAL population in 2010 of just over 130,000. You'll see similar big town, bunch of little towns around cities like San Angelo, Midland-Odessa, Snyder, Lubbock, etc. Pretty easy to find a lot of room to live in the west side. You could sell a 2-1 dump in California and buy a ranch with the proceeds in Texas.
Rural issues - I said Merkel is the 2nd largest town in the county. We have a small police department and a volunteer fire department. We do not have local ambulance support nor first responders. Our tax base can't (or won't) support it. The training and certifications required pretty much rules out "volunteer" work. These people need to be paid to be on standby. It'll take 30 minutes to get someone to our house, assuming the service in View is not already on a call. They have two busses, last I looked. If you're older, this is a bad situation. Lots of smaller town have these issues so if health issues are a concern, look into this also. Its a concern for us and may force a move.
Larger cities will have significant traffic issues. Depending on where you house and where you work, you can be looking at 30~1 hour or better one way commutes. We lived in Houston in the 90s and my 20 mile commute was right at 60 minutes in the AM and 75~85 minutes in the PM depending on when I left the plant. (out here, the 20 mile run is maybe 20 minutes, less if I wanna).
Distance - some things are a "fer piece". From Abilene, it's 2.5 hrs to Fort Worth, 4 hours to Austin, 6 hours to Houston, about same to San Antonio. Look on the map, it's 453 miles from Abilene to El Paso. And we're 200 miles west of Dallas which is 180 miles from Texarkana. For some LOL, Corpus to Texline is 764 miles. El Paso to San Diego CA is only 744 miles. Consider that as the crow flies, it's 711 miles from Washington DC to St. Louis. In non-pandemic times, it's no big deal to jump in the truck on a Saturday and run over to Fort Worth to do some shopping, maybe stop at Uncle Julio's for dinner and run home. About 400~500 miles in a day trip. People run to the Oklahoma casinos for day trips or the weekend all the time. If you live rural, expect to put some miles on your vehicles. Distance is just part of living here.
Car stuff - we have a very active car scene around here with several car clubs. Lots of cruises and shows during the year. Again, a lot of those are 50~60 miles from here to there, so stuff like my 4.56 gear street/strip car would be trailered. Cruisers no problem. Lots of freeways and good quality state highways to places. 75 MPH (80 real deal) on the interstates, 70 MPH on state roads with few exceptions. The climate is dry west of Fort Worth which is good for storage, finding cars no rusted to hell and preservation of tools and such.
Midland/Odessa - it was a mad house for a long time. Until Russia and the Saudis got in a piss fight which killed the price of oil. Texas needs barrel prices in the 50~60 range for fracking to work economically. They are there now, but a lot of consolidation has already occurred. West Texas is home to 1000s of wind turbines and that industry also has some good paying jobs. Life in the oil patch is limited and everybody knows it. Still, we sit on more reserves than the largest fields in the world. One note - we're sloppy about it. Recent surveys show that west Texas is leaking enough methane into the air from equipment, uncapped wells and misc stuff to heat at least 2 million homes/year. That's just bad business.
Texas you pay more in property tax but no tax on your working income or SSI/retirement. Most food items are not taxed, fast food is taxed. State sales tax is 8.25%, maybe .25% more in places. 2% of that is retained local. Auto purchases are taxed at 6.25%. If you own a business, you will pay Business Personal Property Tax on things, you'll need to see the Assessor forms for details. We pay tax on a race car and some misc equipment since we work that as additional income.
Couple of words on NM
State highways are 65 MPH (we're faster!)
Property taxes are indeed lower. HOWEVER - they tax you on EVERYTHING. Food, fast food, income, SSI/retirement income, etc, etc. Everything is taxed. In looking to relocate for retirement, Texas property tax vs NM property tax with est tax on SSI/retirement income is nearly equal. So you don't necessarily get something for nothing.