Let’s look at the entire section
402.050 Who may solemnize marriage — Persons present.
(1) Marriage shall be solemnized only by:
(a) Ministers of the gospel or priests of any denomination in regular communion with any religious society;
(b) Justices and judges of the Court of Justice, retired justices and judges of the Court of Justice except those removed for cause or convicted of a felony, county judges/executive, and such justices of the peace and fiscal court commissioners as the Governor or the county judge/executive authorizes; or
(c) A religious society that has no officiating minister or priest and whose usage is to solemnize marriage at the usual place of worship and by consent given in the presence of the society, if either party belongs to the society.
I don’t see any wiggle room to worry about