NEW YORK (Reuters) - Marco Rubio, the youthful Republican presidential hopeful who touts himself as the candidate of his party's future, has been making moves to court a socially liberal faction of his party that represents gay conservatives.

The Florida senator's staff have held quarterly meetings with the Log Cabin Republicans "going back some time", their executive director, Gregory Angelo, told Reuters. The meetings with the advocacy group were to discuss legislation, issues and opportunities to "partner on," Angelo said. Rubio's office declined to comment on the meetings.

The discussions highlight the tricky electoral math for Republican presidential aspirants like Rubio.

The Republican party will struggle to win the White House in 2016 if it relies only on the support of socially conservative voters. At the same time, presidential candidates will battle to win their party's nomination without those voters, who often dominate state primaries, or early voting contests.

That tension is starkly apparent on gay marriage. For years, staunch opposition to gay marriage was a reliably safe strategy for Republican candidates. No longer.

Facing an electorate that has sharply altered its views on the issue since the turn of the century, even Rubio, who has long opposed gay marriage, has softened his rhetoric, saying last week that he would attend a gay wedding of a loved one.

And then in an interview with CBS's "Face the Nation" on Sunday he said he believed "that sexual preference is something that people are born with" and is not a choice for most people.

While those kinds of comments might help win votes in the general election if he becomes the Republican nominee, they have the potential to antagonize the conservative Republican base he needs to win the primary, party activists said.

"To the right it sounds mealy mouthed, and to the left sounds patronizing," said Martin Cothran, a senior policy analyst for the socially conservative Family Foundation of Kentucky.

CHANGE IN ATTITUDES

Rubio risks alienating people like Bob Vander Plaats, the head of The Family Leader in Iowa, whose endorsement is coveted by many Republican presidential hopefuls each election cycle.

“There’s a lot to like about Marco Rubio,” Vander Plaats told Reuters.

Vander Plaats said he wanted to hear specific strategies from the Republican candidates on how to fight gay marriage. Any attempts to straddle the issue would be a problem for him, he added.

While calling attendance at a gay wedding a personal decision, "I probably wouldn't be going" to a same-sex ceremony, he said. "That shows me endorsing and supporting something that I frankly really disagree with."

Rubio, a Roman Catholic who often talks about his faith, has long defined marriage as between a man and a woman and said that it should be left to the states to regulate marriage. Asked whether his comments over the past week represented a softening in his views, a Rubio spokeswoman, Brooke Sammon, said his position was "clear and well-established."

The Log Cabin Republicans' Angelo said, however, that Rubio was "not as adamantly opposed to all things LGBT as some of his statements suggest." The staff meetings did not include Rubio, he said.

The group has also met with Republican presidential contenders: former Hewlett-Packard CEO Carly Fiorina earlier this year and Senator Rand Paul and Wisconsin Governor Scott Walker, both in 2013.

Paul has sought to differentiate between traditional marriage and civil contracts, while Walker said at the weekend he had attended a wedding reception for a gay relative.

Efforts by Rubio, Paul and Walker to add nuance to their views on gay marriage could play well with some younger Republicans, even if it proves unpopular with social conservatives.

Among likely Republican primary voters, 68 percent oppose gay marriage, according to Reuters/Ipsos data. By contrast, 49 percent of Republicans aged 18 to 29 support same-sex marriage, while 41 percent oppose it and 10 percent are undecided.

The split is much higher among all Americans 18 to 29, regardless of political affiliation. Seventy-eight percent support gay marriage, with 15 percent opposed and 7 percent unsure.

Data from the Pew Research Center show how quickly that change has come about: In 2003, 51 percent of people born in 1981 or later supported gay marriage. By 2014, that number had jumped to 67 percent.

"It would be a very stupid move, in my opinion, politically for the party or the candidates to hold onto" opposition to gay marriage, said Pat Brady, a former chairman of the Illinois Republican party. Brady stepped down from the post in 2013 in part because of his stance on same sex marriage.

Even among many Democrats, attitudes have only recently changed.

Hillary Clinton herself, the Democratic front runner, has a history of distancing herself from the issue. “For me, marriage had always been a matter left to the states,” she said in an NPR interview last year.

But this month, Clinton issued a statement saying she hopes the Supreme Court rules in favor of same-sex marriage. On April 28, the justices will hear oral arguments on whether there is a constitutional right to gay marriage. A ruling is expected in June.

With that case pending, gay marriage is almost certain to come up an event on Saturday hosted by the Iowa Faith & Freedom Coalition. Among the speakers will be senators Rubio, Paul and Ted Cruz, as well as Walker and other Republican hopefuls.