For many opponents of same-sex marriage, the fight has just started.

While supporters of marriage equality celebrate the supreme court’s historic decision in Obergefell v Hodges, advocates for traditional marriage have redoubled their efforts to influence policymakers. But the fight takes place in an unfamiliar political landscape, one where gay marriage has become the law of the land and one of the traditional benchmarks of the social conservative cause has been rendered meaningless.

No matter how ardently Republican candidates for president in 2016 proclaim that they believe marriage is between one man and one woman, the supreme court has ruled differently. So the issue for social-conservative voters is what to do now and how to tell whether candidates are sincere on the issue, and determined to fight it, or just “checking a box” with an intent to leave it alone.

In terms of policy to pursue, the key tactical divide in the Republican Party is whether to emphasize religious liberty laws, designed to protect bakers who don’t want to make cakes for gay weddings, or to instead directly challenge the supreme court and pursue a constitutional amendment to overturn its ruling.

Iowa-based conservative radio host Steve Deace is in the first camp.

“I really don’t care about [a] constitutional amendment any more – not going to happen,” he said, adding that conservatives have “allowed support for a constitutional amendment to become someone’s ‘check the box fig leaf’” when it has “a snowball’s chance in a really warm place” of succeeding.

Instead, Deace wanted to know if candidates are serious about “protecting religious freedom and religious liberty”. In particular, he is concerned that candidates have the capacity to articulate the importance of this issue.

“You can be great on this issue,” he said, “but if you cannot communicate this issue, in the [political and media] environment we’re in, we’re done.”

Others are for going after the supreme court. In particular, former Arkansas governor and presidential candidate Mike Huckabee has used some heated rhetoric to accuse the court of “implementing judicial tyranny”, comparing its actions to those of King George III.

This willingness to challenge the judicial branch has been echoed by others, including the Princeton professor and prominent conservative thinker Robert George. He compared the court’s decision in Obergefell to the Dred Scott decision of 1857, which said black people could not be US citizens, and counselled its simple rejection.

To some conservatives, there is nothing particularly revolutionary in challenging the court. One well-connected GOP strategist based in the south pointed out a parallel on the left in the backlash to the court’s 2010 ruling to gut campaign finance laws in Citizens United. He noted that while Democrats are claiming Obergefell is the law of the land, they are still fighting the court’s ruling in Citizens, using it as a campaign issue and pushing for a constitutional amendment.

The strategist expressed contempt at what he perceived as liberal hypocrisy on the subject, saying: “If you tell us to sit down and shut up about gay marriage, you sit down and shut up about Citizens United.”

Others favor an “all of the above” approach. The social conservative activist Bob Vander Plaats, for example, said he saw presidential campaigns as “laboratories for ideas on how to move forward on religious liberty, holding the court in check and upholding the law of nature and nature’s God on marriage”.

Vander Plaats said he thought candidates needed to be willing to lead on such issues, “not just check-mark the right box”, and offer specific “action steps”.

In a fiery speech on Thursday night in Washington, the “check the right box” attitude drew particular scorn from Rick Santorum. The former senator from Pennsylvania, who finished second in the Republican primaries in 2012 and is now running for the White House again, took aim at those who condemned the court’s decision but were willing to “move on”. They were hypocrites, he said.

If you tell us to sit down and shut up about gay marriage, you sit down and shut up about Citizens United Republican strategist

Santorum proclaimed: “If you believe this is a tyrannical act of oligarchical judges, an affront on first-amendment rights and destructive of the basic building blocks of society and you say it’s time to move on, why are you running for president?”

He made clear he would not move on, and said: “This decision will not stand.”

Santorum’s stance was echoed by the Huckabee campaign. In a statement to the Guardian Hogan Gidley, a senior communications adviser tothe former Arkansas governor, said: “Republicans will never nominate a candidate for president that believes five unelected lawyers have the final say on fundamental issues like life, health and marriage.”

However, not all Republicans see gay marriage as a major issue in future elections. Stuart Stevens, a top strategist for Mitt Romney in 2012, thought gay marriage was “a non-issue” after the court’s decision.

“There’s no difference in the law if you vote for [Iowa Republican] Steve King or Bernie Sanders,” he said.

Stevens went on to argue: “I just don’t see it as an issue that’s going to decide votes.

He also contrasted the issue with abortion.

“You could argue Roe vs Wade will be overturned,” Stevens said. “I don’t think anyone thinks [it] will.”

The push for ‘marriage reality’

Same-sex marriage opponents camp out in front of the Supreme Court in Washington. Photograph: UPI /Landov / Barcroft Media

On Thursday night in Washington, attendees at the second annual gala of the National Organization for Marriage (NOM) did not share Stevens’s attitude.

Members of a group that advocates for “marriage reality”, they seemed ready for a decades-long fight to restore traditional marriage. One speaker, Sherif Girgis, told attendees they were “sowing where we might not reap” and proclaimed: “The truth is going to reassert itself sooner or later; we just need someone to keep telling it.”

Brian Brown, the group’s president, laid out a five-point plan for the group to achieve its goals. This included a push to defeat pro-same sex marriage Republicans, based on the thesis that a pro-gay marriage Republican would do far more damage to the cause than a Democrat who supported gay marriage.

He also advocated for both a constitutional amendment and religious liberty legislation. In particular, Brown said the group would push a bill called the First Amendment Defense Act across the country in 2016. There would be an effort, he said, to push for it to be a ballot initiative in several states, in order to submit the issue to the will of the voters rather than a legislature in which “corporate powers can buy out and intimidate Republicans”.

Brown started his five points with what he considered the most important of them: “electing a pro-marriage president”. Brown argued that the court’s decision could be easily overturned if the replacement of one of the five judges in the majority was named by a conservative president. He noted that this would be a far easier course to pursue than a constitutional amendment.

Brown also argued that merely signing a pledge on the issue wasn’t enough. Candidates, he said, needed to do more.

Moving forward, the question is which path will gain favor: a more populist attack on federal courts or a more narrowly focused and nuanced pushed for what social conservatives view as protections for religious liberty.

But regardless of which approach gains favor, it’s clear that the supreme court has not brought an end to the fight over same-sex marriage.