There have been many groups that have come from the original organization established by Joseph Smith. The largest is the LDS church based in Salt Lake City, Utah--The Church of Jesus Christ of Latter-day Saints. That's the church I grew up in. (I'm from Arizona, which is part of the so-called "Mormon Corridor.") The next largest group is the Community of Christ, which changed its name a few years ago from The Reorganized Church of Jesus Christ of Latter Day Saints. There are several other smaller groups that have broken away at different times. The LDS church and the CoC don't really compete with each other. It's more like curious sideways glances. Most LDS people are very dismissive of the CoC, which is unfortunate. Fortunately, there is now significant cooperation among historians (professional and amateur) belonging to the LDS church and the CoC.
It's fascinating to me to see how the two main organizations growing out of Joseph Smith's original restoration movement have developed and changed over the last 180 years. The headquarters of the two churches are just over 1,000 miles apart. Their approach to many doctrinal, organizational and social issues is even further apart. The most recent example, and the one that has the most resonance with me personally, is the two churches' approach to gay, lesbian, bisexual and transgendered people. (NOTE: I might normally use the familiar LGBT or LGBTQ or LGBTI acronyms, but I'm just using the term "gay" as shorthand here. Personally, I dislike the acronyms SSA and SGA for several reasons, so you won't see them often here on this blog.)
Just a few days ago, the CoC had its World Conference. Their conferences are vastly different from LDS General Conference. The CoC's conferences are much more like the conferences of other Christian denominations. The CoC voted to canonize a revelation which, most notably, fully accepts gay people and endorses gay marriage. This is now scripture in the CoC, Section 164 of the Doctrine and Covenants. For more on this, I recommend John Hamer's excellent coverage and analysis in his post on BCC. Thanks John!
I can't say this definitively because I'm no expert on the Community of Christ, but it seems that they are trying to find a way to really minister to the people. They appear to understand that showing true Christian love is often difficult and challenges our ideas, prejudices, and understanding of the world. The approach of the LDS church (in SLC and most places locally) is focused on "following the prophet" (or more accurately, "following the brethren" even if what they say may be contradictory or unclear) and complying with a restrictive code rather than engaging in a group effort to understand how to love others and help them discover the best part of their humanity. It seems like the CoC is willing to accept that the cost of this may be that some members leave in protest. (There was a rift in 1984 when the church accepted a revelation extending the priesthood to women.) The LDS church has made a similar bargain regarding its political involvement in gay marriage. (Not a few LDS members have become disaffected or resigned their membership altogether over this). The difference is that the latter lacks compassion and a willingness to understand.
I don't think the LDS church will come to a realization that they need gay people in the church anytime soon. In 1978, the church finally realized that they needed people of African descent as well as the members who thought the "priesthood ban" was unjust and racist. And from a simply bureaucratic standpoint, as the church expanded into so many more places in the world, the old regime simply became unworkable. There may come a day when the church realizes it needs the undeniably valuable contributions women would make as holders of the priesthood. What I can't see is how the church can reverse its stance on homosexuality in my lifetime. If it can't do that, then it can't accept gay relationships and gay marriage.
While officially the stance is that the church welcomes gay people so long as they are celibate, that invitation is disingenuous. In some places in the church, two men or two women kissing is enough for formal ecclesiastical probation, or more. The real message isn't celibacy, it's a de facto requirement to "pass" as a completely straight person (whatever that means). The clear meaning of the message is that gay people must be silent and invisible. Call me jaded, but I think that means that the church as an institution doesn't want us at all. I think it needs us. It needs our voice. It needs what we can bring to the table. But it doesn't want us. Hiding and passing as the condition of speaking and contributing renders the invitation hollow and cruel. For a variety of reasons (none of which can be truly reconciled with what Christ himself taught), the church doesn't want us as we really are.
I have contributed time, talents, money, blood, sweat and tears to build up the church for most of my life. I once saw it as the Kingdom of God. I felt good about serving those around me. I felt I had something to offer. I felt invested. Some church leaders apparently agreed since I was giving meaningful responsibilities and opportunities to contribute, both in my youth and as an adult. I even served as a bishop. Most of my callings and other service in the church would have never come about had church leaders and members known about me being gay.
I see no reason to resign my membership at this point. Besides, being Mormon is more than having a membership number. I know of many members of the church who fully accept gay people and try to reconcile their belief in the church with the love they have for their gay family members and friends. I applaud them and thank them. But the LDS church doesn't change due to a critical mass of members doing anything. Unless the top 15 unitedly agree on the need for change, it simply doesn't happen. Just speaking for myself, I can't wait around for that to happen.
So, I'm pretty much done with being an active part of an organization that essentially requires me to be unheard and unseen simply because of who I know I am. Working through the sadness of that is what comes next.