fwiw, here in Connecticut, when you apply for a Justice of the Peace (JotP) position, you are asked if you will officiate gay weddings.
Not for any reason to disqualify you, but to put on the JotP website so that the gay couples have more information in their choice of JotP.
Here in CT, the JotP is a political position, a political appointee by the town's Republican or Democrat committee. (if you are "unaffiliated," the process differs, but not an issue for this conversation) So I would not be surprised about that action regarding the political appointment of a JotP.
However, when it comes to Judges, that is different, very different, to me.
iow, a Judge should be a Constitutional position, not a political position. An equal, but separate branch of government.
The Separation of Church and State.
So, my main question becomes ...
In Texas, does a Judge work for the State or a Church?