“...and protestant groups, which are always subject to the vote of assemblies, thus issues like abortion, euthanasia, women clergy, same-sex marriage tend to split those groups.”
That brief snippet is not universally true. Church polity varies greatly according to denomination.
aMorePerfectUnion:
Really, show me one Protestant Group which does not have assemblies which a theological issue can go one way or the other via a vote of said assembly. If the votes become to controversial, eventually some of those churches that use to belong to that assembly will split away. In my home town, the First Presbyterian Church [a very large one] left the PCUSA a few years ago because of what they saw going on at the National assembly meetings. My guess is more will leave the PSUSA over this recent vote.
The United Methodist are heading down the same direction. My prediction, a major split is coming in that group as well in the next few years.
Even the Southern Baptist have some issues brewing over a Pastor in California stating he will no longer preach on homosexuality as a sin [I think that is the case, but I may be off on the specifics]. I think his son now is stating he is a openly practicing homosexual and now the pastor is changing his tune. Now, if the son is struggling with orientation, then he should be welcomed as any other person struggling with sin, but I think the Pastor is now stating he is changing his understanding on the entire issue. So who knows where even the Southern Baptist are heading in the next few years if more and more of their churches adopt this one in California’s theology.
But SURELY there is some overlap; considering there's 30 or 35 or 50 or 85 THOUSNAD different sects out there...