Whether or not a person goes on a mission is a personal decision for the individual to make after thoughtful consideration and prayer, though there is a greater expectation for young men to serve a full-time mission than for young women.
There has definitely been a shift in The Church of Jesus Christ of Latter-day Saints over the last several years to a “kinder, gentler” view of LGBT people.
Early in the history of the Church of Jesus Christ of Latter-day Saints, Joseph Smith held classes in his home to teach members the doctrines of the Gospel.