The only problem with that is that the GOP is generally pro-business, and environmentalism tends to clash with that.
So we create an environment where environmentalism clashes just as much, if not moreso, with labor, and gets co-opted by the conservatives as a result. You can see some of this in OTL with the fights between environmentalists and the coal industry, which have caused the former Democratic labor stronghold of Appalachia to swing hard to the right, blaming regulations (as opposed to cheap natural gas) for the coal mines shutting down and putting them out of work. Texas' oil industry means that there's little love for environmentalism there.
In other words, for Texas to become a liberal bastion, a key step would be to have an American liberalism that does not identify with environmentalism, and an American conservatism that does. An idea for a late POD would be to heavily alter or prevent the sagebrush rebellion, and especially the Reagan administration's reaction to it. Back in the '70s and '80s, there was a populist movement in the western US opposing the federal management of the vast public lands in those states. While some of the figures in the movement were conservationists and sportsmen who felt that the authorities were slacking in their duties and allowing overgrazing and mining to run amok and destroy the land, many more were themselves ranchers and miners who felt that the government's regulations were too much. It was the latter group of anti-environmentalists that took over the movement, especially after Reagan appointed James G. Watt as Secretary of the Interior. My idea would be to have a dam disaster in the '70s (I'm specifically thinking of the Glen Canyon Dam, which almost failed in OTL in 1983 and would've caused disaster in four states) cause the environmentalists to take over instead, seeing the government's perceived mismanagement of the land and "development for development's sake" as having had severe consequences for people and nature alike, leading to a conservative President in the '80s (I'm assuming Reagan, but given that he's from California, which would've been affected by the Glen Canyon Dam disaster, this could alter his trajectory) either spurning it due to his pro-business leanings or co-opting it due to his small-government leanings. In the former scenario, you've got a western US that's been pulled to the left as a bastion of the environmental movement, which likely wouldn't alter Texas' rightward trajectory much; oil is still king. However, if you get conservative Republicans to instead embrace environmentalism, in a fusion of small government with "small is beautiful"
a la E. F. Schumacher, you could well push Texas to the left as it sees the conservatives as out to destroy their bedrock industry. Related to this, you'd also see Appalachia and Big Coal remain solidly in the Democratic column.
Alternatively, starting from a present-day POD, you could have a future where Texas finds itself ravaged by climate change-induced drought, while at the same time, wind and solar power become big (west Texas has plenty of potential for both). Theoretically, this could produce a robust environmental movement in Texas, and furthermore, one that meshes with the Democrats' pro-development, green energy policies. Couple that with immigration and increasingly liberal cities like Austin and Houston, and you could have a left-wing Texas built on the pillars of environmentalism, urban liberals, and Latinos.