Many states have statutory provisions that provide that children be placed, when possible, in a foster home that matches the child’s religious persuasion; this also tends to cover adoption, and when a child is too young to have a religious persuasion, the law — and, I think, state child welfare agency practice — tends to follow the religious persuasion of the parents. To quote the New York rule, which is actually part of its state constitution,Feel free to post at the Volokh Conspiracy blog -- many non-lawyers do, since it is also a very popular libertarian blog.
When any court having jurisdiction over a child shall commit it or remand it to an institution or agency or place it in the custody of any person by parole, placing out, adoption or guardianship, the child shall be committed or remanded or placed, when practicable, in an institution or agency governed by persons, or in the custody of a person, of the same religious persuasion as the child.Some courts have upheld these statutes (see, e.g., here and here), and I don’t know of any court that has struck them down. The decisions aren’t generally clear on why the statutes are constitutional, but I take it that the arguments are that (1) it’s less disruptive for children who have religious practices or beliefs, (2) it makes religious parents who give up their children feel more comfortable (because they’ll believe that the children’s spiritual needs, as the parents see them, will likely be attended to), and (3) because of consideration 2, it removes one obstacle to parents’ agreeing to put their children up for adoption.
The chief constitutional objections to this, I think, are that (1) it might mean that children from some religious backgrounds have to wait longer to be adopted than children from other religious backgrounds, and (2) it requires the government to decide what religion a parent really belongs to, to decide which religions are close enough to count as being the same religion (a theological decision that the Establishment Clause generally forbids), perhaps to inquire into the adoptive parent’s level of religious observance, and do similar things. I think these constitutional objections are strong ones, but, as I mentioned, courts have not been particularly impressed by them.
Naturally, these statutes are not by any means deliberate attempts to accommodate Muslims as such. They were created to accommodate the interests of Catholics, Protestants, and to some extent Jews, but are now also being applied to other religious groups.
I've blogged about adoption and religion issues several times, like here and here, including a critique of a former post on the subject at the Volokh Conspiracy (see here and here).