I was taught that if you didn’t get married by a priest/minister/rabbi, etc of your faith, before God you were not married, but only involved in a civil contract-I was raised in a traditional Catholic family-I understand that thinking is considered passé by a lot of people, but is still what I believe-and no way would I go to some apostate priest to get married who performed the ceremony for anyone/anything but one man and one woman.
That is your personal religious belief, but as a Texan you know that people in Texas can legally marry privately, with no license and no government or Muslim, or Catholic, or any religious participation.