I would avoid eastern texas, unless you like balls sticky humidity.
Seriously, it sucks living outdoors in the east of texas.
Austin, and the hill country seems legit. There are wild boars that roam. I remember seeing an entire herd of 10 boars crossing a street in the middle of a fairly settled suburban masterplanned community in the middle of the night. I doubt they would be a serious problem if you secure any food cache away from where you sleep.
Bats aren't bad either. Unless they are rabid. Even still, it is easy to avoid them.
I would say Texans are the wildlife you should be most concerned about.
Seriously, tresspassing is frowned upon here, and can be greeted with buckshot to your face. Landowners are allowed to use deadly force if they are endangered by tresspassers, last time I checked.
Even if there is no law, it wouldn't be a problem for Texas bubba to execute you and bury you on the edge of his property.
ALso scorpions west of San Antonio. Nothing a tent or bug bivy can't shield your from.