The US Supreme Court has ruled in Carson v. Makin that states that allow funding to flow to private non-religious schools cannot prohibit funds from also flowing to religious schools. This was a 6-3 decision with Kagan, Sotomayor, and Breyer dissenting.
The Court’s decision seems intuitive enough. Separation of church and state has never meant discriminating against religious institutions when they are in the same space (like education) with non-religious and public players.
As National Review columnist Dan Maclaughlin wrote in his column (linked above), “Allowing students to take state aid to a religious school on the same terms as a secular school does not establish a church, any more than allowing them to use Pell Grants at a religious college or, for that matter, allowing people to buy Bibles with their Social Security checks, establishes a state church.”
So, this is another baby-step towards broader legal acceptance of school choice. All we need in New Mexico is the political courage to actually enact such programs.