Amid the backlash over the controversial religious-liberties law in Indiana, Gov. Mike Pence and other state officials insisted the measure was never intended to permit business owners to deny service to gays and lesbians.

But that is not entirely true.

For the socially conservative organizations that proposed the measure, protecting the right of Christians to opt out of any involvement in gay marriage ceremonies was a primary goal. And they underscored that fact two weeks ago, immediately after Pence (R) signed the measure into law.

“VICTORY AT THE STATEHOUSE!” proclaimed a news release from Advance America, a conservative group whose leader, Eric Miller, was invited to join Pence at a private signing ceremony at the statehouse. “Christian bakers, florists and photographers should not be punished for refusing to participate in a homosexual marriage!”

This week, lawmakers tweaked the law, adding language to “clarify” that it cannot be used by businesses, landlords and others to turn away gay customers. After an outcry by major companies, sports organizations and entertainers — as well as gay activists — lawmakers in Arkansas, Georgia and North Carolina amended similar measures or abandoned them.

Gay rights groups hailed the developments as a significant victory. But they said Republican politicians’ rapid retreat should not be allowed to obfuscate what had been at the heart of the measures: The desire to put a firewall around people who want nothing to do with gay weddings.

“All of this was in reaction to same-sex marriage,” said Jane Henegar, executive director of the American Civil Liberties Union’s Indiana chapter. “That is the context of this bill, what was told to proponents about why they need this bill. For them to back away and say this wasn’t true, I don’t know how they can justify that.”

In Indiana, amendments to the law signed by Pence on Thursday do, indeed, eliminate any protections for business owners who deny gay customers any service, including those related to marriage. However, a new Arkansas law signed by Gov. Asa Hutchinson (R) on Thursday leaves an opening for courts to uphold such a right, gay rights supporters said.

Proponents of the religious-freedom measures do not deny that protecting business owners was one of their primary motivations. But they draw a distinction between turning away individual customers because they are gay and refusing to participate in a gay wedding — particularly for vendors whose services involve a level of creativity.

“Cooking a rack of lamb and putting it on a table in front of somebody is not endorsing anything that you may find in violation of your beliefs” and therefore not something that ought to be protected behavior, said Greg Scott, a spokesman for the Alliance Defending Freedom, a legal nonprofit group that advised Indiana lawmakers.

“But if you’re a wedding singer and somebody says, ‘I want you to lead all the ceremonies for my wedding,’ that’s really a different story, because you are expressing yourself in support and coerced into the celebration of something you don’t believe in.”

An Indiana pizzeria owner who was widely criticized this week for claiming a right not to serve at gay weddings made the same point in an interview on the Fox Business Network.

Gays “are welcome in the store. Anyone is welcome in the store,” said Crystal O’Connor, co-owner of Memories Pizza in Walkerton, Ind. “It is a sin, though, if we condone — if we cater their wedding. We feel we are participating. We’re putting a stamp of approval on their wedding, and we cannot do that.”

In recent years, as more states have legalized same-sex marriage, Christian wedding vendors say they have felt under siege. Several have been sued or punished by local governments for refusing to violate a deeply held conviction that homosexuality is wrong.

In Oregon, the owner of Sweet Cakes by Melissa was fined in February for refusing to bake a cake for a lesbian couple. Last spring, a Colorado judge found that the owner of Masterpiece Cakeshop unlawfully discriminated against a gay couple by refusing to bake a cake for their wedding reception.

And in the case that led the push to pass state-level religious-freedom laws, Elane Photography in New Mexico was sanctioned in 2007 for refusing to shoot a lesbian commitment ceremony.

Most recently, 70-year-old florist Barronelle Stutzman was fined $1,000 last week for violating Washington state’s nondiscrimination law by refusing to create arrangements for the wedding of a longtime customer, a man she has said she considered a friend. A judge also directed her to provide services for same-sex weddings in the future.

The case is now on appeal. Stutzman — who could be forced to pay more than a $1 million in legal fees if she loses, according to her attorney — said she has no intention of backing down.

“It’s about my freedom to be able to work according to my conscience without fear of punishment from the government,” she said in an interview. “They’re trying to bully me into accepting this, and it’s against my faith.”

Some mainstream scholars agree with the premise that the religious beliefs of vendors like Stutzman should be respected under the law.

Daniel O. Conkle is a law professor at Indiana University who supports gay rights and same-sex marriage as well as Indiana’s religious-liberties measure. During a hearing in March, Conkle testified that courts likely would not interpret the law to protect “a religious objector who refuses to serve African Americans, for example, or . . . gays or lesbians, simply because of who the people are.”

But “in narrow circumstances, the result conceivably could be different,” he said, citing as a hypothetical example a Christian photographer. “For some religious people, this sort of participation in a same-sex wedding celebration would violate their deepest sense of religious conviction and conscience.”

Critics of the laws say Conkle is splitting hairs. Refusing any type of service amounts to discrimination, they say, and should not be permitted.

During legislative debate, the Indiana lawmakers who sponsored the measure did not raise the plight of Christian wedding vendors. Instead, they cited last year’s Supreme Court decision in the Hobby Lobby case, which gave businesses the right to refuse to provide certain contraceptives to their workers through company health plans. That case, they said, demonstrated the need to strengthen protections for religious liberties generally.

Asked multiple times by journalists if the law as originally written would give a florist legal grounds to refuse to serve a gay couple, Pence said no. And House Speaker Brian C. Bosma (R) said the original law had been misinterpreted — not just by critics but also by supporters.

“Both the opponents and proponents were indicating they felt that the language allowed a denial of services to gay Hoosiers,” Bosma said. “That definitely wasn’t the intent. Nor do I believe was it the effect.”

Henegar, of the Indiana ACLU, said the politicians have been disingenuous.

She noted that the plight of Christian wedding vendors was raised repeatedly during legislative debate prior to the law’s passage.

Asked at the time to add provisions to make certain that discrimination of all kinds would be strictly prohibited, Henegar said, Indiana lawmakers refused.