As for Crows, the only reason I knew they were listed was because I got reprimanded as a youngster by F&G for shooting at one..
The legality of shooting Crows here in Texas as defined by the TP&W,
Birds
1. Wild Birds: All wild birds that migrate through or are indigenous to Texas, along with their plumage or other parts, eggs, nests and young are protected from harming, killing and/or possession by state and federal law except that European starlings, English sparrows, and feral pigeons may be killed at any time and their nests and eggs may be destroyed. A permit is not required to control grackles; cowbirds; yellow-headed, red-winged, rusty or Brewer's blackbirds; crows or magpies when these birds are considered a nuisance or causing a public health hazard. No birds may be controlled by any means considered illegal by local city or county ordinance.
Protected Wildlife Species in Texas
I have sat out and shot them many times as they would come in to work on various plantings we had put in while I was growing up. They can wipe out a small corn field, or garden, in a VERY short time.
We never went around advertising that we were doing it, and never had anyone come in and warn us against it. We simply did it to try and bump up our harvest rate, and protect what we could. I'm not even going to go into the masses of blackbirds or grackles we managed to get with several well placed rounds of 7 1/2 through a full choke. I will say this though, when they are on the ground in those huge flocks which seeming take half an hour to pass while flying, you can whistle real loud and they will all come right up in a big tight bunch.
Also I was brought up where if you shot it, you had better be prepared to eat it, and my grandmother had a recipe for just about anything that walked, crawled, flew or swam. If there was enough of it left to fry, boil, or bake, you had better not let her know it was left in the field. I learned at a young age, at times there are many things that NEED to be shot to keep other things from being destroyed, and there are other things which will get your backside tanned up right quickly. Also having to clean up a bucket full of backbirds for dumplings, isn't one my fondest culinary memories.
My grandmother however, raised her 10 kids up through the middle and last part of the depression after my grandfather was killed, so putting food on the table was a priority. They were lucky enough to be able to hold on to the family property and worked it as needed to help provide for themselves and others in her neighborhood. I was raised up knowing what eating everything but the squeeler, meant.