As a native Texan, it's weird for a few reasons:
a) Pragmatically, separating from the rest of the United States would be devastating to our economy. Much like the United Kingdom from the EU, but on a much larger scale, because the vast majority of our trade, people, and connectedness come from being part of the U.S. Texans like to trot out the factoid that relatively little land in Texas is owned by the federal government because the feds didn't get any when Texas joined the Union, but the land that is owned by the feds contributes a massive amount to our economy. Metro areas like Killeen and a good chunk of San Antonio would simply cease to exist if the military left. (Never mind that a lot of that oil that Texans are so proud of us dragging out of the ground has to go on pipelines that cross the U.S.)
b) It promotes an "us vs. them" philosophy that's not healthy. Texas tries to hold itself out as separate and, to some extent, "above" the rest of the United States. Yet we get the same two Senators and elect representatives to the same federal House as everybody else. Our way of doing things is not necessarily the right way simply because it's the Texan way. (Our legislature, proudly to some people's way of thinking, only meets once every other year and only for a couple of months. That's a terrible way to govern a state of several million people, especially with a phenomenally weak executive.)
c) When do we move on from trying to live history to remembering it? In order to graduate from college, I had to take courses in both federal and state history (3 credit hours of "HIS 1024 History of Texas I" is on my transcript), just because we're so wrapped up in our own mythology. Yes, Texas was its own country. So was California, and Alaska, and Hawaii. Those are things for the textbooks and to explain weird language on deeds and why so many flags fly over the state capitol. It's not the basis for some inexplicable "independent" streak.
Texas needs to get off its predisposition with its past and look towards its future, preferably being one that doesn't embrace fossil fuels--good job on the wind production, thanks T. Boone Pickens--and a car-focused, sprawling development culture.
I hope it does, though I'm watching from afar, having decamped to Washington State many years ago.