We belong to God. The Bible says that “we were bought with a price.” The Captain of our salvation - our Lord is Jesus Christ - not some Amish leader who sets himself up to be some potentate.
So no, neither we nor they “belong to the Amish” as you said.
We don’t belong to man - we belong to God, although they would like for them to belong to them no doubt.
Yes, as church leaders, they would be within their scriptural right to preach from the pulpit what they wanted to, As in it is a sin to fornicate, but it would be utter arrogance for one of them to say that since you won’t grow a beard, or wear this particular gown or dress, I (as a deacon, elder, or minister of the Amish, or in this particular Amish community) have a right to cast you out.
They have every right to associate in the manner that suits them. If it’s not for you, fine, form different associations and believe as you will, whether that’s following the dictates of some other earthly leader like the pope or lacking a central authority and being more congregational like Baptists. Their way of life is as much cultural as it is religious. Would you force ultra-Orthodox Jewish men to cut their side curls and dispense with the hats? Why not, if not?