Arizona Republican Gov. Jan Brewer, right, vetoed legislation on Wednesday that would have allowed businesses to refuse service to gays and lesbians. (Ross D. Franklin/AP)

Conservative activists said Thursday that they will continue to press for additional legal protections for private businesses that deny service to gay men and lesbians, saying that a defeat in Arizona this week is only a minor setback and that religious-liberty legislation is the best way to stave off a rapid shift in favor of gay rights.

Gov. Jan Brewer (R) vetoed legislation on Wednesday that would have provided a wide variety of religious exemptions to Arizona businesses, after major business groups, prominent Republicans and gay rights advocates argued that it would amount to discrimination.

Many conservatives said they will continue working to convince voters and judges that opponents of same-sex marriage and abortion are motivated by faith rather than bigotry.

“The fight has to be over what the First Amendment is,” said John C. Eastman, chairman of the National Organization for Marriage, adding that his side needs to convince the public that conservatives are not trying to deny the rights of other Americans. “This is not somebody adhering to old Jim Crow lunch-counter discrimination. This is a fundamental dispute about what marriage means, and why it’s important for society.”

Religious-freedom measures that could have implications for gay rights are pending in Kansas, Mississippi, Missouri and Oklahoma. The Supreme Court will hear arguments in a case next month in which two businesses argue that they should be allowed to refuse to give their employees contraception coverage mandated under the Affordable Care Act.

“There is a sense of alarm within the pro-family movement and among conservative Christians that there [are] growing threats to religious liberty, and many of those threats do relate to the agenda of the sexual revolutionaries,” said Peter Sprigg, a senior fellow for policy studies at the Family Research Council.

Louise Melling, the deputy legal director for the American Civil Liberties Union, said the efforts are part of a misguided attempt to preserve an outdated social order. She noted that federal courts have repeatedly rejected biblical claims as a justification for discriminatory action. Cases rejected by the courts have included a Christian school that paid men more than women in the 1980s because men traditionally are the heads of their households, and a South Carolina barbecue chain that defended its refusal to serve black customers in the 1960s on religious grounds.

“At moments of social change, what you see is a resistance, and a desire to create or preserve certain pockets,” Melling said. “Historically we’ve rejected those claims, based on our understanding and deeply held beliefs about religious freedoms.”

The question of religious exceptions has cropped up in a broad range of other cases over the years, with varying outcomes. In Guadalupe Benitez v. North Coast Women’s Care Medical Group, the California Supreme Court ruled that the medical group violated state civil rights laws when a fertility specialist denied treatment to a lesbian. But in another case, Eastern Michigan University paid $75,000 in a settlement with a former student, Julea Ward, who had been expelled from a counseling program because she refused to work with same-sex couples.

Douglas Laycock, a University of Virginia law professor who specializes in issues of religious freedom, said controversy over a handful of cases involving social issues is “creating a public that is hostile to the very idea of religious liberty.”

“The debate has been captured by utterly intolerant people on both sides,” he said. “Everybody wants religious liberty for me, and my opponent ground into the dust.”

The debate over the Arizona bill highlights how far the country has moved on questions of sexual orientation and gender identity in recent years. Although the law did not specifically mention gays, it was spurred in part by court rulings in Colorado and New Mexico — both of which bar discrimination on the basis of sexual orientation — that businesses could not refuse to provide services for same-sex weddings.

The Arizona measure amended the state’s version of the federal Religious Freedom Restoration Act , which passed with broad bipartisan support in 1993 and says that the government may not pass a law that “substantially burdens a person’s exercise of religion.”

At least 30 states have similar religious protections through statutes or their constitutions, and several conservatives question why they are now sparking controversy.

“Five years ago, this would have been seen as innocuous,” said Brian Walsh, executive director of the American Religious Freedom program at the Ethics & Public Policy Center, whose group has established “religious freedom caucuses” in 18 states.

He acknowledged, however, that several of the most recent legislative proposals are focused specifically on same-sex marriage.

“For many people, marriages and weddings are sacred to them, and they want to make their own decisions about how to participate in them,” said Walsh, whose group has advised lawmakers on bills in Kansas and other states.

The Kansas House passed a measure this month that would allow any individual to refuse, on religious grounds, to provide same-sex couples with services. The Mississippi Senate passed a measure in January that allowed individuals and businesses facing discrimination claims to use religion as a defense, but House sponsors of a similar bill said they eliminated that language this week.

Eunice Rho, advocacy and policy counsel for the ACLU, said recent measures have expanded religious exemptions “into a scope not contemplated” by the original federal law. Under the federal statute, someone seeking an exemption would have to prove that the law in question imposed a “substantial burden” on a person’s ability to practice one’s religion; several of the state proposals reduced this test.

It remains unclear how many of these measures will make it into law, given the controversy in Arizona. The president of the Kansas Senate announced Tuesday that his chamber would not take up the House religious freedom bill; Ohio legislators withdrew their measure on Wednesday.

Sprigg said advocates of such protections need to “pause to take a look at their language and messaging, and learn the lessons of Arizona to protect themselves against the attacks that brought down the Arizona bill.”

Eastman said traditional-

values groups must press ahead with legislation so one of these measures can reach the Supreme Court, which he considers sympathetic. He said Brewer got “so cowed” by the criticism from entities, including the National Football League and Sen. John McCain (R-Ariz.), that she didn’t give the courts a chance to “draw that line” between religious freedom and discrimination.

Republican consultant Ron Bon­jean, by contrast, said the veto helped the party as it heads into the midterm-election campaigns.

“Republicans have been burned time and again by a few ‘lone wolf’ Republicans that have hijacked the message and painted our party in a bad light over issues such as abortion and rape,” Bonjean wrote in an e-mail. “Many prominent Republicans could see the danger being seen as intolerant and many wanted to prevent the party from stepping on another political land mine that would have turned off voters across the board.”