The following is from the OP...
Aside from whatever the Texas Statutes say...Texas:
"No religious test shall ever be required as a qualification to any office, or public trust, in this State; nor shall any one be excluded from holding office on account of his religious sentiments, provided he acknowledge the existence of a Supreme Being."
Obviously...if a person running for office made it publicly known that he or she is atheist...then, you're 100% right, voters have control over which lever they pull or which name they punch.
However, I'm a native Texan, been around a few decades...and nobody that I'm aware of has come forward as being an atheist candidate.
Consequently, "as far as I know", there's been no legal challenge before the Texas Supreme Court of the US Supreme Court to rule or make a decision on such. I don't have a clue as to what this current US Supreme Court might say in this situation.
If the First Amendment guarantees freedom of religion...then I think it should also include freedom FROM religion as well.