The Michigan town where only Christians are allowed to buy houses

That question should be irrelevant. The issue here is whether the restrictive covenants in the property deeds are enforceable.

Background: Racial covenants aren't unconstitutional, per se. In Shelley v. Kraemer (1948)[1] SCOTUS simply declared them unenforceable, reasoning that the courts, as organs of the state, couldn't use their powers to achieve the same ends that other state entities were prohibited from doing. In other words, people are free to have contracts and deeds with whatever conditions they want; you just don't get the benefit of a court enforcing the terms.

The exact same logic should apply to covenants regarding religion--specifically, covenants discriminating among religious denominations. (A covenant that limited land to being used by a religious organization of any kind is probably fine.) The only reason I can see for why the status of the township matters is because it's probably the township who would have, historically, asked a court to enforce the covenant. But based on the logic of precedent it wouldn't matter whether the township can legally seek an injunction if the court itself would be prohibited from issuing such an injunction.

Probably the defendant (township?) has spun some ridiculous theory for why Shelley doesn't apply, and to cover their bases the plaintiffs are forced to argue that even if Shelley doesn't apply, then for [reasons] the township would be barred from enforcing the covenant. But such covenants are usually enforceable by neighbors, as well, so if Shelley doesn't apply and courts are permitted to enforce such religious covenants then the plaintiffs will have effectively lost, regardless of whether the township can legally seek enforcement

[1] https://en.wikipedia.org/wiki/Shelley_v._Kraemer

They called it a "resort" several times in the article. It probably has "township" status with some corporate powers.