Texas is the one that comes to mind as the strongest, but it's far from unique in that regard. Louisiana pops to mind next. Other examples of states with very strong cultural identities off the top of my head: Oregon, Utah, Tennessee, Florida, West Virginia, Michigan, Maine, Vermont, New York, Illinois... you get the idea.
I'd say about the half the states have a strong, unique identity. The remainder are similar to their neighbors but the farther you travel the more apparent the differences.
Well, yes. The differentiation is both dumb and well-reasoned, depending on your ethics.
However at least germany and austria have meaningfully distinct languages or dialects and many centuries more to marinade in their differences. Texan and californian aren't distinct enough to produce nationalities that are clearly distinct (aside from arbitrary pride!) and they regularly swap populations sufficient enough to provide cultural osmosis that keeps the two cultures tied together.