Pigeons are not game animals in Texas.  They are considered to be feral, invasive, nuisance animals.  There are no state regulations at all governing the trapping or killing of pigeons.

All you have to worry about are local laws. I've trapped a lot of pigeons and never had a problem with anything else getting into the trap. 

If you only use whole corn, your odds of catching any of the protected species are greatly reduced and if they inadvertently end up in the trap simply release them.

Can you imagine anyone being prosecuted for having protected species getting into their pigeon coop?

It would take an extremely liberal tree hugging activist judge to even begin to hear such a case.

I live in Austin, TX.  Home of all the liberal tree hugging judges and others in the good state of Texas.  It would be just my luck to catch a dove in the trap and have one of them arrest me. Heck, they might even try to get me for cruelty to pidgeons. Or, if it happens to be someone affiliated with PETA, then cruelty to dogs for training them to hunt. 

This is meant to be sarcastic, but we truly do have an inordinant amount of liberal tree huggers in Austin, so it is not all joking.