The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
Given the context, it’s reasonable to assume the Supreme Court (especially today’s court) would hold that the first amendment is specific about Congress not establishing religion and therefor is open to interpretation by the states.
Unless you have a specific case law regarding the application of the first amendment to state legislation regarding religion, I’m not seeing how The Due Process law is relevant.
I really want to know so I’ve ’done my own research’.
Here’s the closest cases I could find. It seems reasonable here that the Supreme Court has historically ruled in a way that specifically objects to Oklahoma’s legislation. I’m convinced that you’ve offered relevant material yet I’m still 50/50 on the matter with today’s Supreme Court. If Thomas were off the bench, I could see it ruled otherwise.
The case centered on the limits of school vouchers offered by the state of Maine, which had disallowed the use of vouchers to pay for religious-based private schools. In a 6–3 decision the Court ruled that Maine’s restrictions on vouchers violated the Free Exercise Clause, as they discriminated against religious-backed private schools. The minority opinions argued that the decision worked against the long-standing principle of the separation of church and state, since state governments would now be required to fund religious institutions..
[Roberts] wrote that the Maine legislature excluded “private religious schools from those eligible to receive such funds” and that such exclusion separates of church and state more than intended under the Establishment Clause of the United States Constitution. He wrote that, on the basis of Zelman, “a benefit program under which private citizens ‘direct government aid to religious schools wholly as a result of their own genuine and independent private choice’ does not offend the Establishment Clause.”
The lawsuit was initiated when a group of Ohio taxpayers filed an action against Susan Zelman, the superintendent of public education in Ohio, arguing that the program violated the Establishment Clause. Simmons-Harris, along with other residents of the Cleveland area, argued that the government “could not pay tuition for students to attend religious school”.
Chief Justice Rehnquist delivered the majority opinion, which held that the school voucher program was not in violation of the Establishment Clause. The ruling also determined that government support for religion is constitutional if it does not occur de jure but de facto, and if the use of religious facilities is neither specified nor encouraged. Cleveland’s program was declared to be religiously neutral and to be giving parents the benefit of true private choice.