Just because there's sand and water don't mean it's a beach...lol.... I wouldn't swim in Galveston to save myself from drowning , its so filthy
If you want clear water drive a couple extra hours from Corpus to South Padre -- that's where Texas water starts getting really nice.
The water around Galveston is clean -- it's just silty/ brown from the Mississippi. Galveston can have nice blue-green water in the spring -- there are many pictures of it.
Spoiler The water on the gulf coast, though typically a rich "Chocolate Yoo Hoo", is actually relatively clean. On some spring and fall days, the water is nice and green and you can clearly see your feet while sitting on your board. There aren't too many issues with localism and the vibe is pretty mellow. For more on surfing in Texas, check out the following links: link
It's my favorite beach. They keep the beach clean. It's never so busy that its uncomfortable. The town is nice with plenty of good places to eat. And, it's not an expensive place to stay. We go 3-4 times per year.
It's not polluted. It's brown color is due to the inability of fresh water to convert to salt water quickly. So the fresh water sort of bands together in the 2,300nm outflow. If the majority of the outflow shifted towards Florida instead of Texas, we'd have the turquoise waters while they get the brown silted water.
If you are going with intentions to swim, head south. If you are going just to be on the beach, cool out, drink & eat, Galveston is just fine. Hell, after half a day of drinking, you wont care about how the water looks.