I’m not quite a native Texan, but I’ve lived here for my whole adult life. On purpose, too. 
Texas pride is interesting stuff. We know our schools are not the best and our politics are not the most civilized. We know that our landscapes are not the prettiest, even though a great green hill speckled all over with bluebonnets is a sight to make the heart ache.
Still, we do have a rich history and a well-deserved reputation for being stubborn, proud, independent, tough, and friendly. In some ways we’re like Borogravia in Monstrous Regiment: “They’re not the most beautiful mountains, but they’re OUR mountains!”
Many Texans really hate being called on this and will thoroughly and dogmatically defend their home state. I am very guilty of this: I get very defensive when my state is characterized as an ignorant backwater. The people who say this mostly have never been here or have not been here in, say, forty years. There’s ballet and theater and museums and art in Houston and Austin and Dallas. There is even (or was, twelve years ago) a surprising burgeoning little artist community in Corpus Christi, the city that time forgot somewhere in 1974.
I love it here and I’m proud of being a Texan. I get teased for it by my Canadian friends and I tease right back: just like I wear cowboy boots and a cowboy hat and ride a horse to work every day, they live in igloos and drink moose milk.
We have a damn weird sense of humor. My father, native Texan and avowed coonass, was made an Admiral in the Texas Navy when he retired from the US Navy. He was made so by then-Governor George Bush. I believe part of his commission is permission to take the USS Texas out for a spin whenever he wants to.
I often relate, with my usual perverse pride, the story of how the Democrats of the Texas House of Representatives escaped the state under cover of night to avoid a vote to gerrymander their districts. It’s a ridiculous-but-true story that sounds more like a Coen Brothers movie than reality (for that matter, by the way, No Country For Old Men has as perfect a rendering of small town Texas as I’ve ever seen).
But Texas separatists? They exist but they’re pretty rare and get filed under the same mental heading as UFOlogists for most of us – relatively harmless, most of the time, and kind of off.
Oh, and a lot has changed in the last forty years. I learned a good deal about pre-Western civilizations in Texas history. I do remember hearing some interesting stories about the Carancahua, for example.