Among the alliance’s successes has been bringing cases involving relatively minor disputes to the Supreme Court — a law limiting the size of church signs, a church seeking funding for a playground — and winning rulings that establish major constitutional precedents.

But it hopes to carve out an even wider sphere of protected religious expression this term when the justices are to hear two more of its cases, one a challenge to a California law that requires “crisis pregnancy centers,” which are run by abortion opponents, to provide women with information on how to obtain an abortion, and another in which it represents a Colorado baker who refused to make a cake for a gay couple’s wedding.

While the abortion case is the latest legal volley in a generation-long battle by social conservatives to limit the effect of Roe v. Wade, the Colorado baker’s case, which the court will hear next month, will test whether groups like the alliance can persuade the court to similarly blunt the sweep of Obergefell v. Hodges, the ruling that enshrined same-sex marriage into law, as well as the anti-discrimination laws protecting gay men and lesbians.

If there is a battle somewhere to restrict protections for gay men, lesbians or transgender people, chances are the alliance is there fighting it. The alliance has defended the owners of a wedding chapel in Coeur d’Alene, Idaho, who did not want to perform same-sex ceremonies. It has tried to stop a Charlotte, N.C., law that gave transgender people the right to use the bathroom of their choice. It backed the failed attempt by the Arizona legislature in 2014 to allow businesses to cite religious freedom in turning away same-sex couples.

Image Alan Sears in 2014. He is one of the founders of Alliance Defending Freedom and was its longtime president until recently. Credit... Samantha Sais for The New York Times

“We think that in a free society people who believe that marriage is between a man and a woman shouldn’t be coerced by the government to promote a different view of marriage,” said Jeremy Tedesco, a senior counsel and vice president of United States advocacy for the group, which is based in Scottsdale, Ariz. “We have to figure out how to live in a society with pluralistic and diverse views.”