From the Introduction (my emphases):
Amici... wish to emphasize that principles of religious freedom lying at the heart of our system of ordered liberty also strongly support the right of gay men and lesbian women to marry.
People of faith have come to a variety of conclusions about same-sex marriage. Many churches and clergy, as a matter of doctrine, withhold formal recognition of same-sex unions within their religious liturgy. Others, including the Episcopal Church in California, may permit clergy to bless same-sex relationships without necessarily bringing them within the rite of marriage. Still others, including congregations of the United Church of Christ, Unitarian Universalist Association, and Metropolitan Community Churches, readily include same-sex couples in their rites of marriage....
Before this Court Proposition 8’s Proponents have abandoned any contention that Proposition 8 advances religious-liberty interests. Yet their amici have submitted briefs insisting that same-sex couples’ right to marry somehow threatens Californians’ religious liberty, and that Proposition 8 is a reasonable response. In truth, according same-sex couples the same right to civil marriage that other Californians enjoy poses no real threat to the religious liberty of faith traditions limiting religious rites of marriage to mixed-sex unions. For even if civil marriage is recognized as a fundamental civil right of all people, religious organizations always have been free – and remain free – to frame their own rules restricting who may be joined in a religious rite of marriage.
Some churches, for example, will not permit the divorced to remarry in a religious ceremony. Some clergy decline to officiate interfaith marriages. No one can force them to. But the government ought not mandate that anyone’s civil marriage shall be void for failure to conform to theological doctrines or church rules governing religious marriage rites.
According equal marriage rights for all in our civil law threatens no one’s religious liberty. Allowing same-sex couples the legal right to marry threatens the religious liberty of Catholics, for example, no more than does allowing civilly divorced citizens to remarry in contravention of Catholic doctrine. Same-sex couples’ civil marriages threaten the religious liberty of those who oppose such unions in their churches and synagogues no more than interfaith marriages threaten the religious liberty of those who interpret their scripture and tradition to prohibit such unions.
No one can force clergy of any denomination to solemnize any wedding that conflicts with his or her faith tradition, and no church, synagogue, or other place of worship loses its tax-exempt status for refusing religious rites of marriage to citizens possessing a civil right to marry. Though Proponents’ amici suggest that Proposition 8’s demolition of same-sex couples’ right to marry was designed to protect Californians’ religious liberty, quite the opposite is true. The real threat to religious liberty comes from enforcing as law the religious doctrines of some sects, to outlaw marriages that others both recognize and sanctify. .... Amici respectfully submit that Proposition 8 unlawfully deprives many Californians of a fundamental right merely because of who they are, that it denies them equal protection of the law, and that it does so at the expense of religious freedom.
The complete brief (as well as the other amicus briefs on our side) here.
H/T Susan Russell