Christofferson, whose brother is gay, was involved in creating an LDS Church-sponsored website, mormonsandgays.org, which includes video clips of Mormon leaders as well as LGBT members and their families promoting compassion and understanding toward gays, and encouraging everyone to be "disciples of Christ."
Not that many in the 15 million-member Church of Jesus Christ of Latter-day Saints know about the site, Christofferson acknowledged, despite numerous news stories about it.
"It has been underutilized," he said.
But the church is working on "refreshing and expanding the site in the next few months," he said, and the updated version will be more broadly advertised.
The hope is that LGBT Mormons will feel valued by their religious community, he said, "so they don't feel they have to find fulfillment elsewhere, or that they can't find love, brotherhood and sisterhood within the church."
What does the LDS Church think of members who back same-sex marriage?
"There hasn't been any litmus test or standard imposed that you couldn't support that if you want to support it," Christofferson said, "if that's your belief and you think it's right."
Any Latter-day Saint can have a belief "on either side of this issue," he said. "That's not uncommon."
Problems arise only when a member makes "a public, sustained opposition to the church itself or the church leaders and tries to draw others after them," he said, and that support swells into "advocacy."
Fellow apostle Dallin H. Oaks also praised the church's website and efforts on behalf of gay members.
But Oaks, a former Utah Supreme Court justice, wasn't sure apologizing for past language on homosexuality would be advisable.
"I know that the history of the church is not to seek apologies or to give them," Oaks said in an interview. "We sometimes look back on issues and say, 'Maybe that was counterproductive for what we wish to achieve,' but we look forward and not backward."
The church doesn't "seek apologies," he said, "and we don't give them."
Oaks, too, reaffirmed the need for more civility in public debates toward all sides on these issues.
"The teaching effort that we've engaged in today," he said, "is a very important part of what we hope our members will hear in the way of being more civil, with those who disagree with us on some fundamental principles and also more firm in insisting on our right to hold our views."