once they can get their own fucking house in order
This is the fundamental problem right here. There is no house. There are neighborhoods worth of houses. Some of them not even next to each other. Some of them share outdated morale codes. Some of them have moral codes you and I could both respect. They are no more in control of each other than we are of them.
It is one of the definite weaknesses of all the separate denominations. If there was only one Christian group, we could try to talk with the Pope and the other Patriarchs and potentially have them all heard the group in the same direction.
Just think of the Westboro Baptists, so shameful that even the KKK denounced them on their home page a few years back.