- The state is prohibited from giving the money to the religious entity. Funding the religious organization is an Establishment Clause violation.
- The state is required to give the money to the religious entity. Refusing to fund the religious organization, when other comparable organizations are funded, is a Free Exercise violation.
- The state can choose whether to give the money to the religious entity. There is "play in the joints" between the Free Exercise and Establishment Clause issues, and states can choose how they want to resolve that tension.
Today, in Carson v. Makin, the Supreme Court took a big step towards Door #2. The Court struck down a Maine program which (for certain rural areas lacking public schools) funded private schools, but only if those schools are non-sectarian. If Maine is offering parents funds to send their kids to private schools generally, it cannot withhold those funds if the parents elect to send their children to a religious academy. Religious schools must be eligible for generally-available funding on the same basis as any other "comparable" private school.
In making this ruling, the Court distinguished (and significantly narrowed) an older case, Locke v. Davey, where the Court upheld a program which excluded ministerial training from an otherwise generally available scholarship program. The Carson Court said Locke was limited only to circumstances where the school was specifically training ministers; not "religious education" more broadly.
This got me thinking, however, about what options are still available to a state like Maine which is perhaps leery about sending its tax dollars to directly support religious education. Carson does not directly say "states must fund religious education" after all. It merely says that states must allow religious schools to obtain funding when they would otherwise be eligible based on the general criteria the state uses for assigning funds.
So imagine the following rule: "No school shall be funded unless each of its employees is fully subject to anti-discrimination rules." The state, it is fair to say, has a strong interest in ensuring that the subjects of its funding abide by and are protected by anti-discrimination rules. Still, anti-discrimination law contains certain exemptions, one of which is known as the "ministerial exemption" -- ministers are not subject to anti-discrimination protections. In Hosanna-Tabor Evangelical Lutheran Church and School v. EEOC, the Court expanded who counts as a minister beyond the proverbial priest or Rabbi to include many teachers at religious institutions -- these teachers now cannot sue if they are the victims of discriminatory conduct. Religious schools are relatively likely to have such "ministers" on the payroll, so they would run afoul of the neutral rule, and would not be eligible for state funding.
Whether this gambit will work depends a lot on how it is phrased and the degree to which courts are willing to accept it as a neutral rule (which, in turn, may relate to whether there are other schools whose eligibility for state funds would be limited by the rule for reasons having nothing to do with religion). But -- on about an hour's worth of thought -- it seems like a plausible argument.