The left end of the spectrum is occupied by the progressives. The most radical of these are the LGBTQ activists, who are engaged in acts of disobedience personally and corporately. They mean to make The UMC endorse their vision of full inclusion and full endorsement of their agenda by any means necessary. The less radical of the progressives don't actually disobey the rules, but they endorse rule-breaking in the name of their causes. Many progressives have simply discarded the Bible as a source of teaching and practice; one I read on Facebook recently referred to it as "the damn Bible."
Next in from the left, but still very far from the center of gravity of the denomination are those who call themselves "Centrists." This is very shrewd rhetoric on their part, since it makes them look reasonable; however, they are almost as far left as the progressives, with whom they have many cordial and productive relationships. These are the folks who keep coming up with the same re-structuring and accountability proposals that a) would give the progressives everything they want under the name of Unity, and b) have been rejected by the last several General Conferences and/or the whole UMC voting on proposed constitutional amendments. Many centrists say they are evangelical, or used to be; many claim a high regard for the Bible. That said, they have a way of making the Bible say what they want it to say, or dividing it into parts that are authoritative and parts that are not. In this way, they function as apologists for the radicalism of the progressives.
These are mostly young people. They have grown up surrounded by progressive ideas in school and on campus. They are heavily invested in the current culture. They see themselves as enlightened. They are generally in favor of the ideas of the progressives and centrists -- especially since they have rarely encountered any others except in cartoon form -- but they are less inclined to fight for them in the context of The UMC. There are cooler churches out there for those who want to do church, so they often drift over to those.
The Family Loyalists
Next in, we have those whose minds have been changed on sexuality issues because someone they know and love very much has "come out" in some way. In my experience, grandparents are especially likely to make this adjustment. In most ways, the Family Loyalists are very ordinary Christians. Many have taught Sunday School and VBS for years, and would normally think of themselves as Bible-believing Christians, in so far as they know the Bible. But they have a blind spot where certain people are concerned. They just cannot look their beloved in the eye and say they can't agree -- or risk their relationship, if the beloved should reject them. In any split, these folks are more likely to stay with the main branch of the denomination, whether they agree with it or not.
Birthright Members/the Oblivious
The true center of the UM spectrum are the people who have gone to church all their lives, often in the same congregation or one very much like the one they grew up in. For them, all the kerfuffle beyond where they worship and serve is mere sound and fury. They may be distressed about it, even disapprove of it, but so long as their congregation continues to operate, they will concentrate on that relationship. Theologically, these folks are probably pretty traditional. Some know the Bible pretty well, but considering how little anybody knows the Bible any more, they probably haven't grappled much with the issues that convulse the church from both right and left. Unless they are forced to make a choice, these folks will remain members of the main branch of the denomination in any split.
The Church Loyalists
Moving now toward the right, the more conservative end of the spectrum, we come to the church loyalists. These are people with some theological acuity. They know what they believe, and they know the Bible. Whether they were brought to faith in Christ through The UMC or joined it later, they are very conscious of their choice of churches. Commitment is a big deal to them. They made promises and those promises mean something to them. They have stuck with The UMC out of conviction, despite many shocks and provocations. Living by the rules matters to them, too, and they are not happy with those who break the rules and expect to get away with it. They have had many opportunities to leave The UMC and go elsewhere, and they have been tempted, but remain out of obedience. In case of a split, they would carefully consider joining the more conservative successor church, but they might also consider it a duty to stay and witness where they are.
The traditionalists are generally conservative, and probably in more than one sense. They uphold the beliefs and practices of the Church they see as semper, ubique, et ab omnibus -- that which has always, everywhere, and by everybody been believed and practiced. They know what they believe, and they are opposed to the progressives, root and branch. They are often politically conservative as well. They make common cause with the orthodox and evangelicals to uphold traditional social and ecclesiastical mores and institutions. They are less attached to The UMC than the Loyalists are, but are not detachable to just any, more conservative replacement. In a splintering of The UMC, they might leave, but would be as likely to join an Anglican or Lutheran or some other church, rather than the conservative successor denomination arising out of our division.
This group usually caucuses with the evangelicals and is often confused with them as the same kind of church members. They are not. They believe the Bible, but do not define it in quite the same terms as the self-identified evangelicals do. They believe in the authority of the Bible quite as much as the evangelicals, however, and they insist that the Bible be interpreted by sound exegesis based upon a thorough understanding of the ancient cultures out of which it sprang. They care about creeds and confessions of faith and all the great definitions the Church has arrived at in her history. Most are Anglican/Arminian in orientation (Methodists being derived from that stream of Christianity), but a fair number are enamored of German theologians and speak from a more Reformed point of view. They stick with The UMC so long as The UMC's official doctrinal statements and rules are capable of an orthodox presentation. In any split, they would be likely to go with the conservative branch; however, doctrine really, really matters to them, and they are sometimes uncomfortable with evangelical slogans and wonder how that would translate into actual church discipline.
Many apply the term "evangelical" to themselves; I am here referring primarily to the more doctrinaire evangelicals. They are very prominent in the conservative action groups that have networked to resist the progressives, especially in matters relating to sexuality: Good News; the Confessing Movement; the IRD. Their bottom line is biblical obedience. Their weak point is a tendency to confuse the evangelical sub-culture and its slogans with the faith once delivered to the saints. In the last twenty years, evangelicals have reached out beyond their own camp and made common cause with others -- especially the orthodox -- and this has been a cause of their success. Evangelicals would take the lead in forming any new, more conservative denomination that arose out of a splintering of The UMC; whether that new denomination embraced the bulk of the former denomination and renewed it or became another version of Free Methodism or something similar is yet to be seen.
The above spectrum represents my perspective and is limited in that way, especially since -- as an American United Methodist -- my perspective is skewed toward the U.S. church. How well these categories describe United Methodists in Africa, Asia, and Europe is another question. Most African UMs are evangelical in their theology and function well in partnership with the orthodox and evangelicals of the American church; however, their experience of the world also makes them care about things that rarely show up on Americans' radar. My opinion is that the more Americans and Africans learn to include each other's perspectives and concerns in each other's plans for the future, the more likely any new, more conservative denomination would be saved from becoming a kind of "refugee camp for the faithful remnant."