The notion that a public servant can decline to provide a service because they disapprove is arrogant, self-centered, self-righteous, unnecessary, obnoxious and probably unconstitutional.
I'll bet that there are more than a couple who object to a Christian woman marrying a Jewish man. Same thing. And while I am at it, how come no one seems to have a conscientious objection to third or fourth marriages? What about a wife who is (obviously) very pregnant? Would the same “logic” not apply? Are they not religiously offended?
We get it. The conservative Christians who are so prominent in Texas don't approve. That's their problem, not ours.
Texas being Texas there are a number of bills pending that intend to make sure that gays know that they are second-class citizens. For example, HB 2876 would allow wedding vendors to discriminate against same-sex couples, and HB 3571 would allow just about any business to refuse to serve gay people if the business owner thinks that Jesus would be offended. There are other bills kicking around as well.
Those flag-waving “patriots” should know that nothing is more un-American than discriminating against a minority group. Religion never justifies discrimination.