WASHINGTON — For conservative Christian groups, Monday’s Supreme Court ruling protecting the rights of gay and transgender workers was not only the latest sign that they are losing the American culture wars over sexuality. It also caused widespread concern that it could affect how they operate their own institutions.

Many faith-based organizations, like schools or nonprofits, do not allow L.G.B.T. people to work there, citing religious beliefs that sex should only be between a man and a woman who are married.

“No question it is going to make it harder to defend our religious freedom, as far as an organization being able to hire people of like mind,” said Franklin Graham, who leads Samaritan’s Purse, a large evangelical relief group.

“I find this to be a very sad day,” he said. “I don’t know how this is going to protect us.”

The employment of L.G.B.T. workers in religious institutions has been an issue across the country. In recent high-profile cases, teachers at Catholic schools in Washington State and Indiana have said they were forced to leave because of their sexual identity.

In a 6-to-3 ruling on Monday, the Supreme Court determined that Title VII of the Civil Rights Act of 1964, which bars employment discrimination based on race, religion, national origin and sex, also applies to many millions of gay and transgender workers.

The ruling would have “seismic implications” for religious freedom and would potentially set off years of lawsuits for religious organizations, said Russell Moore, the president of the public policy arm of the Southern Baptist Convention.

“There’s a common assumption in secular America that as the culture changes that evangelicals and Roman Catholicism and other forms of religion will morph and change along with it,” he said. “I don’t think that is true.”

He added, “Most evangelicals and Catholics and others who hold to a traditional Christian ethic are countercultural.”

The Association of Christian Schools International, which provides services to about 2,700 schools in the United States, is reviewing the implications of the case, and reiterated its position that sexual activity must only be between a man and a woman who are married. The group’s president, Larry Taylor, said that “the impact on the hiring policies of religious institutions that teach the biblical view of marriage” and that “uphold a standard of conduct consistent with our faith” is “not yet fully understood.”

For religious conservatives, the ruling was especially pointed because it came from a bench that leans conservative, and because Justice Neil M. Gorsuch, whom they had championed as a hero for other causes like abortion, wrote for the majority. Unlike the 2015 Supreme Court decision that legalized same-sex marriage nationwide during the Obama administration, this ruling came from their allies.

In his opinion, Justice Gorsuch recognized the existence of several religious freedom protections, including the First Amendment, the Religious Freedom Restoration Act of 1993 and a 2012 Supreme Court ruling that recognized a “ministerial exception” in employment discrimination laws.

But he signaled that Monday’s decision could lead to a fight over the validity over those protections. “How these doctrines protecting religious liberty interact with Title VII are questions for future cases too,” he wrote.

In his dissent, Justice Samuel A. Alito Jr. suggested that some existing religious protections could unravel. “The scope of these provisions is disputed, and as interpreted by some lower courts, they provide only narrow protection,” he wrote.

He also said the ruling left open questions about access to restrooms and locker rooms. “For women who have been victimized by sexual assault or abuse,” he wrote, “the experience of seeing an unclothed person with the anatomy of a male in a confined and sensitive location such as a bathroom or locker room can cause serious psychological harm.”

Some religious groups, including the United States Conference of Catholic Bishops and the public policy arm of the Southern Baptist Convention, had filed amicus briefs in two sets of cases that were before the court, arguing that Title VII did not address gender identity. The 1964 law “prohibits employment discrimination based on race, color, religion, sex and national origin.”

“I am deeply concerned that the U.S. Supreme Court has effectively redefined the legal meaning of ‘sex’ in our nation’s civil rights law,” the president of the Catholic bishops’ conference, Archbishop José H. Gomez, said in a statement. “This is an injustice that will have implications in many areas of life.”

“Protecting our neighbors from unjust discrimination does not require redefining human nature,” he said.

But what conservative religious groups may see as a religious freedom issue, secular and progressive religious groups see as an excuse to discriminate.

The Interfaith Alliance’s policy director, Katy Joseph, called it “a watershed moment for equality,” and the executive director for the American Humanist Association, Roy Speckhardt, said it was a sign that “even with the religious right entrenched in Washington, D.C., progress can still happen.”

Forecasting a coming fight over religious liberty, Americans United for Separation of Church and State urged a unified strategy. “The progressive, inclusive faith and secular communities must come together to make clear that religious freedom is a shield that protects, not a sword that licenses discrimination,” the group’s president, Rachel Laser, said in a statement.

Even as more Americans have embraced the cause of gay rights, sexuality remains one of the most divisive issues in Christian communities. This year a group of leaders in the United Methodist Church, which has roughly 7 million members in the United States, announced a plan to formally split the church because of “fundamental differences” over same-sex marriage.

Bishop Cynthia Fierro Harvey, president of the Council of Bishops for the United Methodist Church, said on Monday that she appreciated the Supreme Court’s decision.

“We have faithful followers of Jesus who both stand on very opposite interpretations of L.G.B.T.Q. issues,” she said. “My hope is that at some point we will look at ways that do honor and respect people for all that God has called them to be and do.”