Practically speaking, and in the short term perhaps. But if we are to remain a nation of laws, the government, local, state and federal must obey the law as well. That includes the highest law.
The Texas Constitution does allow the Legislature "to to regulate the wearing of arms", but Article VI of the federal Constitution makes that Constitution supreme. So, if the 14th amendment applied the protections of the Bill of Rights against the states, and that was clearly the intent as understood both by its proponents and opponents, then the Second Amendment over-rides that power granted to the the Texas Legislature by the state's Constitutution.
The Suprem Court itself has stated that law which are in violation of the Constitution are no laws at all and no one is obligued to obey them, no court may enforce them.
"All laws which are repugnant to the Constitution, are null and void." Chief Justice Marshall, Marbury v. Madison, 5, U.S. (Cranch) 137, 174,176