I'm guessing Texas is an at-will state, but just going to a show of any kind in your private time should not be a firing offense no matter where you work. I don't care if you work for the Southern Poverty Law Center and go see a minstrel show on Saturday. You're doing it on your private time.
Religious institutions have a little more freedom in certain areas regarding who they can hire and fire depending on their job duties.
For instance, a preacher for a Baptist church can be required to be Christian as a condition of their employment. But they can't fire a janitor for religious reasons because their faith has no impact on the work they perform.
For teachers, they probably have a policy regarding public support of the church and its doctrines that was violated when the teacher posted about attending a drag show.
It's stupid, but it's legal.
I have similar restrictions at my job in municipal government. I'm not allowed to get involved in local politics or advocate for or against candidates openly. As a public official, I'm always at least somewhat on duty.
Hell, I have to be careful about what I text, because my personal phone is subject to Open Records requests.
Seriously, though, are people still pretending Christian organizations are filled with decent human beings? You can just point to the majority of western history as an example of the kind of people running these orgs.