From the trial court's judgment giving the father custody, Dexter v. Dexter, no. 2005 DR 0110 (Ct. Com. Pl. Portage County, Ohio May 1, 2006), aff'd, 2007 WL 1532084 (Ohio App. May 25):
[Mother] has undertaken to engage in a lifestyle that is extreme by normal social standards and [mother] testified that she is a devotee of sado-masochism; that she is bisexual; that she engages in paganism; that she has used illicit drugs on a semi-regular basis; and that she spends a great deal of time online where she has two to four websites of so-called "blogs." The evidence also indicates that her fiance ... also engages in sado-masochism, and in the past produced and starred in a theater troupe depicting such activity while also engaging in such conduct in his private life with [mother]....
[M]other and her boyfriend have a perfect right to engage in sado-masochism, paganism and their chosen sexual orientation, but nevertheless, this Court is not convinced that [they] would exercise the due diligence that is required to engage in those practices without exposing such lifestyle to the parties' child[ and thus] adversely affect[ing]the best interests of [the child, a 4-year-old girl].
The father may indeed have been a more suitable parent on some grounds, for instance if the mother and her fiance indeed used illegal drugs (though note that the drug use is listed as just one item among many, including the paganism), or if the mother's online time materially affected the time she spent with her daughter (though I assume that if the mother's problem was that she left her daughter unattended, for instance, the court would have said that rather than just pointing to her "spend[ing] a great deal of time online"). But the reference to mother's paganism — and the view that pagans may be denied custody because their open practices risk "exposing such lifestyle to [their] child[ren]" — strikes me as a clear First Amendment violation.
It seems to me that her bisexuality should likewise be none of the court's business; nor should her sado-masochism, unless there's some specific evidence that the practices are physically harmful to her and thus indirectly to the child (evidence that judgment, the magistrate's findings, and the appeals court decision never even hinted at). Likewise, reliance on the fiance's theater performances seem to me barred by the Free Speech Clause. Still, even if we set the sexual practices aside, perhaps on the theory that Lawrence v. Texas provides only modest protection for sexual autonomy (a hotly debated question), the First Amendment bars a court from relying even in part on the mother's pagan religious beliefs or open participation in pagan religious rituals (except insofar as some specific conduct during those rituals endangers the child or perhaps the parent, something there's no evidence of here).
For more on courts restricting pagan practices (there, Wiccan practices), see this post and the Decree of Dissolution of Marriage, Jones v. Jones, No. 49D01-0305-DR-00898, at 4 (Feb. 13, 2004) (directing both parents "to take such steps as are needed to shelter [the child] from involvement and
observation of these non-mainstream religious beliefs and rituals"), rev'd, 832 N.E.2d 1057, 1061 (Ind. Ct. App. 2005). For information on courts discriminating against parents who are less religious and less observant than their ex-spouses, see this post. For more on the general issue of child custody decisions that restrict parents' speech, or that count parents' speech and religious belief against them, see my Parent-Child Speech and Child Custody Speech Restrictions, 81 NYU L. Rev. 631 (2006).
For more on the Ohio Court of Appeals decision in this case, which does flag the possible impropriety of relying on religion and the like, but which also suggests that considering religion as a factor is permissible, see the UPDATE at the end of this post.