To add to jimrtex, I'd point out the low voter turnout of the more working-class Hispanics who live in places like Pasadena.
Galveston used to be the closest thing Texas had to a "labor Democrat" stronghold because there were so many longshoremen; the advent of container shipping and the shifting of cargo away from Galveston to the Port of Houston ended that era. So today their economy depends more on the University of Texas medical school and the various hotels, restaurants and bars that make up their tourism industry. Hurricane Rita in the mid-2000s was a big setback for them too. Basically they're a pretty stagnant place that is getting progressively smaller and older as time goes by - and more Republican. They still tend to provide some of the most plaintiff-friendly juries in Texas, though; I work for a plaintiffs' law firm and Galveston and Beaumont are by far our favorite places to try cases.
Does that have anything to do with what was going to trial locally. For example, a local hospital with a history of surgeons operating drunk or some otherwise slam dunk negligence cases recurring at the loading docks?
No, it's because the population is almost monolithically working class and predisposed to identify with employees and workers rather than with management and the company in such cases. They probably know someone who got injured in some physically demanding job and know how devastating it can be, economically, emotionally, financially and physically. It doesn't matter if they're socially conservative or not, if they're Democratic or Republican, they're going to have more empathy for the plaintiffs in those cases.
When you request a jury pool and go through voire dire, the defense counsel is going to try to get as many white collar types on the jury as possible - people who are middle class or better, who went to college and who have never worked the sort of job where you have to wear safety equipment. They'd rather have a politically liberal doctor than a machine shop worker with McCain/Palin stickers on his truck. In someplace like Galveston or Beaumont, there aren't enough "defendant-friendly" people living there, so it's going to be hard to get enough of them on a jury.