By Ginger Gibson and Emily Stephenson

CLEVELAND/WASHINGTON (Reuters) - Donald Trump's choice of Mike Pence as his vice presidential running mate has irked some Republican activists who see the Indiana governor's years of opposition to gay rights initiatives as a setback to efforts to broaden the party's appeal.

The pick could bolster Trump's support among religious conservatives, but it also opens up a new line of attack for Democrats and liberals seeking to paint the New York businessman as a divisive candidate, putting at risk his efforts to woo moderate voters ahead of the Nov. 8 election against Democrat Hillary Clinton.[nL1N1A10HR]

Rachel Hoff, the first openly gay member of the Republican Party's platform committee, has spent time in Cleveland ahead of next week's party convention trying repeatedly to get the party to change its official position on gay marriage and adoption by gay couples. She was dismayed by the choice of Pence.

"After the Pence announcement, I think the question is - is Trump really moderate on gay rights issues? It seems more likely his rhetoric has been a smoke screen," Hoff said. "There's no substance behind it. By picking Pence, Trump is signaling his administration may not be any friendlier to the LGBT (lesbian, gay, bisexual and transgender) community."

Megan Robertson, a Republican strategist in Indiana who has pushed for the party to be more open to gay members, was similarly disappointed.

"Picking Pence shows that he maybe doesn’t care about that community as much as he tried to profess that he did,” she said of Trump.

Clinton's campaign seized on the announcement to attack Pence's record on gay rights issues, saying it "embarrassed" the people of Indiana. Clinton has previously called Trump the most divisive candidate "in our lifetimes," referring to his calls to temporarily ban Muslims from entering the country and to deport millions of undocumented immigrants.

In 2015, Pence found himself at the center of a national uproar when he signed a bill that he said was meant to protect religious liberty, but which critics countered would allow business owners to deny services to gay people.

After intense pressure from liberal groups and large corporations, he asked lawmakers to clarify that businesses could not deny services on the basis of sexual orientation, calling it a "subject of great misunderstanding."

He has also fought against same-sex marriage and allowing gay people to serve openly in the military. A U.S. Supreme Court ruing last year legalized gay marriage nationwide and the Pentagon in 2011 ended the ban on openly gay and lesbian people serving in the military.

In 2009, while a member of the U.S. Congress, Pence argued against expanding the definition of a hate crime to include sexual orientation, calling it an attempt to "advance a radical social agenda." The federal hate crimes law was expanded to make this inclusion.

DIVIDED PARTY

Gay supporters of Trump are hopeful Pence will have little influence on a potential Trump administration.

Trump has declared himself the most gay-friendly candidate in the election. He expressed support for the gay community after a mass shooting at a gay nightclub in Orlando in June that killed 49 people, and broke from his party during an argument about transgender bathroom usage, saying people could use the bathroom of their choosing at his office building Trump Tower in New York.

That has cheered moderate Republicans who have been seeking to appeal to younger, more liberal voters.

"Donald Trump is the nominee of the party and Donald Trump is going to set policy," said Chris Barron, who has launched LGBTrump, a group seeking to encourage gays to vote for Trump.

Pence, 57, comes from a different wing of the divided Republican Party than Trump, one that is dominated by evangelicals in southern and midwestern states. Conservatives were elated with his selection.

"It's the best conservatives could possibly want," said Brent Bozell, a conservative leader.

The pro-gay rights group Log Cabin Republicans said it would seek to pressure the Republican Party at the Cleveland national convention to adopt a more gay-friendly policy platform, including by running a full-page ad in a local paper.

The party's platform committee met early in the week to draft official policy positions on myriad issues. The document, which carries little significance beyond the symbolic, calls for a constitutional amendment to reverse the Supreme Court's decision legalizing gay marriage and included a veiled acceptance of gay conversion therapy, a practice that has widely been criticized as harmful to children.

Despite the disappointment that gay rights activists are feeling, Log Cabin Republican president Gregory Angelo said he thinks voters are going to look at Trump's past statement on gay rights and not where Pence stands. Trump has spent little time talking about social issues and has instead focused on immigration and economic issues.

"Donald Trump rose to stardom as our presumptive nominee because he showcased an opposition to illegal immigration and unfair trade deals. That's what's resonating with the Republican electorate this year," he said.

(Reporting by Ginger Gibson and Emily Stephenson; Editing by Richard Valdmanis and Frances Kerry)