Suri is apparently treated as an adult, free to make decisions on her clothes, make-up and diet.If we assume, for the purposes of discussion, that Cruise follows a religion-based approach to child rearing, involving maximum autonomy, and Holmes now objects to that and wants to raise the child according to more conventional decision-making and discipline by the parent, how much of a factor should that play in determining custody? Should Cruise's ideas about child-rearing have more weight or less weight because they are premised on religion?
Scientology expert Rick Ross explained to the Daily Mail's Alison Boshoff last year: 'Scientologists treat kids as if they are individuals capable of making their own decisions.'
Indeed, Tom echoed this approach in an interview in 2010.
'I say to Suri, "I really want you to eat this protein if you’re going to have that sugar,"' he said.
'She looks at me and she goes: "Dad, I don’t think you should try to force me to do something I don’t want to do."'...
Just last week, an evening of pizza and ice-cream with her mother ended in tears when Katie took her daughter's cone away.
That is, imagine Cruise2, a man with the same approach to child-rearing, arrived at through religion-free thought processes — philosophy, common sense, personal experience.... While you're at it, imagine Cruise3, with the same notions of child-rearing, premised on religious beliefs, with a much more conventional religion. Let's make Cruise3 a mainstream Protestant who has come to a serious conclusion about children, individual autonomy, and free choice based on a deep commitment to the teachings of Jesus.
ADDED: USF lawprof Paul L. McKaskle emails:
My course materials on Comparative Civil Liberties (a comparison of European and American law about freedom of expression, association and privacy) discuss this issue. A European Court of Human Rights held that religion cannot be a factor in deciding custody (Hoffmann v. Austria,  17 E.H.R.R. 293) where the mother and father were married in the Catholic Church but the mother converted to Jehovah's Witness and the Austrian Courts denied her custody for that reason. As to what would happen in the United States (at least as of 2009, the date of the course materials) the course materials summarize as follows:
“On the issue of whether the religion of one parent can be dispositive of the issue of custody, there is little law in the United States. The issue has never reached the U.S. Supreme Court. In California, two older intermediate appellate court cases involving a Jehovah's Witness parent come to opposite results. In Wilson v. Wilson, 137 P.2d 700 (1943) the religious issue appeared to be the dominant factor in the trial court's decision to give custody to the father, who was not a Jehovah's Witness. The appellate court affirmed. In Cory v. Cory, 161 P.2d 385 (1945), the appellate court (without mentioning Wilson, supra) reversed the trial court which had awarded the father custody in preference to the mother, primarily on the basis that the mother was a Jehovah's Witness. (The trial court's reasons were mostly directed at whether the children should be allowed to pledge allegiance to the flag at school, which the father wanted and the mother did not.... Neither case was reviewed by the California Supreme Court, so, technically, a trial court in California could follow either case. There was a third California case, Quiner v. Quiner, 59 Cal.Rptr. 503 (1967), in which the trial court refused to give custody to the mother who belonged to a religious sect (the Exclusive Brethren) in which voluntary association with non-members of the sect or any activities outside the family were strictly forbidden. This meant, according to the trial court, that the child, inter alia, could not attend movies, have school friends outside the sect, engage in school athletics or even have a record player. The Court of Appeals, in a 2-1 decision, reversed and awarded custody to the mother on the grounds that her religion should not be a factor in awarding custody (citing Cory, supra, but not mentioning Wilson, supra.). The California Supreme Court granted a hearing on the case on its own motion. This is an extremely rare occurrence in California, but it had the effect of vacating the Court of Appeals opinion so that it [is no longer] precedent. According to the attorney for the mother, after the hearing was granted the Clerk of the Supreme Court contacted both him and opposing counsel on several occasions and said the Chief Justice (Roger Traynor at the time) “wanted the case settled.” The parties did settle shortly thereafter and the further review in the Supreme Court was dismissed. (That did not restore the Court of Appeals opinion, however. Once it had been vacated it was no longer precedent.)”[The Quiner case has been cited in law review articles on the topic–written by non-California judges, lawyers or students–under the erroneous assumption that the case is good law because it is published with a citation in the West Publishing Company's California Reporter. West publishes Court of Appeal cases in the California Reporter when they are first filed and they remain there even if they have subsequently been vacated. But such a case does not appear in the Official Reporter and, even though there is an "unofficial" citation available for such a case (as is set out above) it can no longer be cited as authority.]
On a related issue, the power of a divorced parent to raise children in his or her religion, the courts have reached conflicting results. Some courts have held this power is vested exclusively in the custodial parent. See, e.g., Marjorie G. v. Stephen G., 592 N.Y.S.2d 209 (1992). More courts have held that even the non-custodial parent has the right to expose the children to his or her own religion. See, e.g., Felton v. Felton, 418 N.E.2d 606 (Mass. 1981); Mentry v. Mentry, 142 Cal. App. 3d 260 (1983).
I realize this doesn't answer your question of what should the law be. I think it can be an allowable a factor, analogous to Prince v. Massachusetts, 321 U.S. 158 (1944) which held that the state may intervene in protecting the health or safety of a minor despite parental religious beliefs. In my opinion the oddball grant of "autonomy" has a bearing on the child's health. And, of course, if there is joint custody, the mother certainly has an equal right to impose her child-rearing approaches (as long as they were not dangerous) while she has custody.
(In the now vacated Quiner case, when the appellate court reversed and gave the mother custody, it did grant the father some visiting rights which, presumably, would allow the son to associate with others not a member of The Exclusive Brethren during such time-including, of course, his father-and engage in non sect-related activities-including going to movies with his father, for example. All of this, of course, would be completely contrary to the teachings of the sect.)