Through the due process clause of the 14th Amendment. Im often surprised at the confidence people have in their understanding of Constitutional law and the moving target of Supreme Court precedent. Also, much Constitutional law isnt found in US founding documents, including the 1st Amendments application to states. Like much Constitutional Law, we can thank or condemn the Supreme Court for its current state. Absolutely not determinative but the following is a USSC endorsement of Jeffersons sentiment.
Neither a state nor the Federal Government can, openly or secretly, participate in the affairs of any religious organizations or groups, and vice versa. In the words of Jefferson, the clause against establishment of religion by law was intended to erect "a wall of separation between church and State." Reynolds v. United States, supra, at 98 U. S. 164. Everson v. Board of Education, 330 U.S. 1 (1947)
Im not sure how this Court will ultimately decide this case if it ever has the case before it, but whether it can stand constitutional scrutiny is not settled law