I actually think Alito may have been the one to ask the critical question, about whether religious schools that failed to recognize same-sex marriages would lose their tax exemptions.
Iirc the Catholic Parochial schools are the largest category of religious schools in the country. I don’t think it’ll be lost on either Kennedy or Roberts (the other potential swing vote) that Vitelli saying they would lose their statuses would really mess up the Catholic schools.
Six members of SCOTUS are Catholic or at least claim to be.