I've both dived and sailed in the Gulf. The posters above are right, the brown water is from silt, a little farther offshore (or laterally, away from a river delta) it's green, which is pretty good, and farther offshore it's blue, which is clear and great swimming and diving.
For example, the Flower Garden Banks National Marine Sanctuary, about 90 miles offshore from you, is almost clear as gin--great diving.
Bear in mind that the murky water tends to be fresh, and hence lighter than the heavier salt water from offshore. Frequently, divers will dive through this murky fresh/brackish water layer for 20-30 feet, then find the clear layer of salt water deeper down. While you will be sailing on the murky (lighter) brackish layer on top. So it mostly has to do with river and bay runoff. Go out past that, and you're almost in the Caribbean (or the "Redneck Caribbean")...