While almost all birds are protected, non-native birds aren't. These include European Starlings and House Sparrows which were brought to this continent against their will. Grackles are protected though! The most violations (unknowing, probably) occur from cutting down dead trees, which often contain nests. (cutting in late fall or the winter is probably OK)
The MBTA is the legislative version of the four treaties that the U.S. has signed (with Russia, Canada, Mexico and Japan). It acknowledges that birds don't recognize international boundaries, and several countries often share responsibility for protecting a single species. The treaties were the products of destructive trends to adorn womans hats and other clothing with large feathers, almost resulting in the extinction of several species.
The MBTA is enforced by the U.S. Fish and Wildlife Service, whose local agents are called Game Wardens, and in north Texas are under the auspices of the Texas Parks & Wildlife Dept. Game Wardens are federal officers and can enforce TPWD regulations too.