Keep in mind, Texas has 31 (depending on the source) species of sparrows. ALL but the English/house sparrow are technically protected. Granted, in good chunk of the state, if you are shooting sparrows, chances are you are shooting house sparrows. I would say, please don't shoot sparrows around grassland areas. There is a dang good chance then that you may be shooting sparrows that area declining rather rapidly.
So yall have the regulation---
--The only birds not protected by any state or federal law are European starlings, English sparrows, feral rock doves (common pigeon, Columba livia) and Eurasian collared-doves; these species may be killed at any time, their nests or eggs destroyed, and their feathers may be possessed.
--Yellow-headed, red-winged, rusty, or Brewer's blackbirds and all grackles, cowbirds (does not include cattle egret), crows, or magpies may be controlled without a federal or state depredation permit when found committing or about to commit depredations on ornamental or shade trees, agricultural crops, livestock, or wildlife, or when concentrated in numbers and in a manner that constitutes a health hazard or other nuisance.
Back in 2011, I got to learn way more about cattle egrets than I ever wanted to know about them due to the Carrollton egret situation. Somehow, even though I can't stand them, I'm now one of the go to folks one egrets and heronry management (really wish I was joking about that). One of the first questions I always got was if they aren't native, how are they covered under the MBTA. Heck, they weren't even nesting here until the 50's. Yell, unlike most of out other invasive bird species, cattle egrets got here on their own due to range expansion. They pretty much have the largest range expansion known.--Other little nugget, the USFWS did NOT want to add them, but some folks pushed the right buttons.
Now, there has been some limited movement legislatively to get them removed from the MBTA, but it tends to stall. Most of the representatives don't understand how the law works, and usually try and turn around and tell the local (say Fort Worth city staff) to "do something". Well they can't it's a federal issue. When they finally do see the light and start working on it, they discover that the MBTA is literally one of the toughest laws on the book to change simply due to that third letter. Once they discover everything that is involved, they either can't find a co-sponsor (the usual case), or they simply drop it.