Young spoke Saturday night to about 400 people attending the New Frontiers conference of the group Affirmation: Gay and Lesbian Mormons.
The former BYU quarterback said his goal "is to build bridges with my gay brothers and sisters. We need to see each other as Jesus sees us."
Young also reminisced about winning the Super Bowl with the San Francisco 49ers, and spoke about relying on faith.
"(Faith is the) fundamental fuel for the human experience," he said. "If the experience is to return to our Heavenly Father, faith is the fuel from beginning to end."
He introduced his wife, Barb, as an advocate for the gay, lesbian, bisexual and transgender community.
"There is not a day that goes by that you are not on her mind. She has spent countless hours advocating for you," Young told the crowd.
Barb Young, a Mormon convert whose older brother is gay, actively opposed California's Proposition 8 in 2008, even though leaders of the Utah-based Church of Jesus Christ of Latter-day Saints enlisted members to work for its passage. The measure banning same-sex marriage was passed by voters.
She urged attendees to be "patient like Jesus" and to love LDS church members as they move toward understanding of their LGBT family members.
"One of the most beautiful things about this church is that it can evolve," she said. "It may not go as fast as everyone wants, but it is evolving."
In the end, Barb Young said, everything depends on how fully Mormons live their faith.
"If we consciously embrace Jesus' teaching of empathy, compassionate, and love, the future world will be different," she said.
Judy Finch, who has a son and two grandchildren who identify as being gay, said she sees mostly LDS church members in her private practice as a psychotherapist.
"In my role (as a therapist) I provide hope and reassurance and encouragement," Finch told the crowd. "Heavenly Father loves our gays exactly the way they are—exactly the way he created them."
Perhaps people have been praying for the wrong thing when they ask for gay people to become straight, she said. Instead, they should ask to know God's will in "respect to gays" and for the ability to fulfill it, she said.
The conference revolved around a theme of spiritual healing and reconciliation for those who identify as being LGBT.
The Mormon church teaches that same-sex attraction is not a sin, but acting on it is.
"Even though individuals do not choose to have such attractions, they do choose how to respond to them. With love and understanding, the church reaches out to all God's children, including our gay and lesbian brothers and sisters," the church website states.