When I read Wireman v. Perkins, digested here, I thought the underlying constitutional questions were interesting. While not mentioning this recent Kentucky decision about religious upbringing of children in the child custody context, scholar Eugene Volokh's analysis here of constitutional issues in custody questions indicate the Kentucky Court of Appeals reached the correct result. Some quotes from Child Custody Decisions and the Constitution:
The Supreme Court's 1984 Palmore v. Sidoti decision is an excellent example: The Equal Protection Clause bars a judge from granting custody to one parent instead of another based on the other parent's having entered into an interracial relationship (or marriage). And this is so even if the judge sincerely (and perhaps even reasonably) believes that a child might face more social problems if the child is reared in a mixed-race family.
Likewise, many state courts have held that judges can't restrict a visiting parent's exposing his children to his own religion, even when the custodial parent is teaching a different religion, at least in the absence of a showing of likely serious harm to the child. A judge may theorize, perhaps even plausibly so, that it's better for children to learn one religion rather than two rival ones. But he can't implement his theory through an order restricting one parent's teachings, since that would violate the Free Exercise Clause.
Several state courts have similarly held that judges can't hold a parent's lack of religion against him in a child custody proceeding -- again, even if the judge sincerely believes that it's in a child's best interests to grow up in a more religious home. The Establishment Clause bars such preferences.
It seems to me these courts are quite right. Indeed, a parent's Due Process Clause right to have custody of the child may have to give way in divorce cases, since both parents can't live apart and at the same time live together full time with the children, and since even joint legal decisionmaking for the child may be impossible when the parents are unable to get along; but this reason for restricting parental rights generally doesn't justify restrictions on Equal Protection Clause, Free Exercise Clause, Establishment Clause, and Free Speech Clause constraints on the government.
Likewise, perhaps even these constitutional constraints must give way when genuinely necessary to prevent likely serious harm to the child, on a sort of "compelling government interest" rationale; I'm skeptical of that in many instances (see my Parent-Child Speech and Child Custody Speech Restrictions, 81 NYU L. Rev. 631 (2006)), but I see the force of the argument. But I don't think that a simple desire to serve the child's best interests slightly better (in the family judge's view) justifies departing from the constitutional constraints.
That's why I'm so troubled when some family courts do prefer the more religious or churchgoing parent over the less religious or churchgoing parent, in my view a blatant violation of the Establishment Clause. That's why I'm troubled when some family courts restrict parents' teaching their children various disfavored ideologies, whether racism, Communism, support for the propriety of homosexuality, hostility to homosexuality, support for the propriety of polygamy, Wiccanism, and so on. And that's why I'm troubled when family courts suggest that parents could be penalized because they don't teach their one-quarter Korean children things that all-white children needn't be taught, or because they don't live in sufficiently "divers[e]" neighborhoods.
A family court judge necessarily has broad power over children's (and therefore parents') lives. It doesn't follow, though, that this power should be entirely free of the Equal Protection Clause, Establishment Clause, Free Exercise Clause, or the Free Speech Clause.
UPDATE:From Marcia Oddi of Indiana Law Blog,
Our COA in 2005 threw out a provision in a decree which read "That the parents are directed to take such steps as are needed to shelter [the child] from involvement and observation of these non-mainstream religious beliefs and rituals[.]" The trial judge inserted it on his own, upon finding out that both parents were Wiccans. The Indiana CLU sued. The COA threw out the provision on non-constitutional grounds. The trial court judge was recently appointed to the COA by our Governor. Here are the links.