Texas law covering common law marriage or cohabitation will make the courts very busy.
Anyone who is married and not yet divorced and has been living together with another can be charged with polygamy unless they have a Cohabitation agreement.

Living together is grounds for the state to declare a common law marriage.
This could get a large percentage of the population of Texas arrested.

Texas is only going to prosecute "Mormons" for these offenses, never Baptists. It is Jim Crow Justice.

Texas amended its marriage and consent laws a couple of years ago, openly announcing it intended to make FLDS religious practices illegal. UT Attorney General Shurtleff was used as a consultant to make sure the changes were as FLDS-hostile as possible. This was blatantly unconstitutional, but don't hold your breath. Everyone up to and including the Supreme Court is unlikely to enforce the Constitution if only "weirdos" are affected.

"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof;" (First Amendment to the Constitution, extended to the States by the Fourteenth Amendment).

"The test may be stated as follows: what are the purpose and the primary effect of the enactment? If either is the advancement or inhibition of religion then the enactment exceeds the scope of legislative power as circumscribed by the Constitution. That is to say that to withstand the strictures of the Establishment Clause there must be a secular legislative purpose and a primary effect that neither advances nor inhibits religion." ( Supreme Court in Abington School District v. Schempp, 1963)