Since the goal of these people is to take over societal institutions in order to normalize sin, they will not leave.
The problem is that these folks are leaches. Similar to the non-procreative nature of homosexuality, the pro-homosexual religionists do not grow.
They feed off of those who do grow.
That's the problem with evil. Once it has infested and taken root in these organizations, any attempt to oust them will be portrayed as those of extreme right-wingers. Should they split, with the true Methodists forming anew, they will be branded as extremists who have broken away from the "real" Methodist church.