Tex. Fam. Code § 2.601

A religious organization, an organization supervised or controlled by or in connection with a religious organization, an individual employed by a religious organization while acting in the scope of that employment, or a clergy or minister may not be required to solemnize any marriage or provide services, accommodations, facilities, goods, or privileges for a purpose related to the solemnization, formation, or celebration of any marriage if the action would cause the organization or individual to violate a sincerely held religious belief.