You can conceal carry in Texas parks now, if you have a license. Rarely a reason to, though.

Big Bend...been there something like 50ish times. My avatar is one of the sunsets. There, you will be dealing with Mexican Black bears which are small, flighty, and not threatening. You will be lucky to see one. I was checked out by one in my sleep, under my tarp....the smell woke me up. It wandered off, I never got out of my bag. They tend to hang around the park employee village dumpsters, up in Pine Canyon, and along the South Rim loop.
They have steel bear boxes in all the campsites. Use them! I've only heard about the occasional tent/pack ravaging when folks didn't use proper food storage.
They have mountain lions there as well. There has been the odd attack from sick cats, none lethal, again you'll be blessed to see one.
For a very short time, I carried a pistol when hiking in BB....it's heavy, and in reality, useless, since there is not much in that park that's going to "get you".