I do not understand your statement on Stone-Campbell and Irish restorationists.
As a member of a Church of Christ congregations for a very long time. I and the congregations I have been in have always professed that if any one followed the biblical teaching of salvation they were a member of the body of Christ.
The Irish version of the restorationist movement began many years after the American version, with the same goal in mind.
Their itinerant preachers came to America and began to make converts. Many of their doctrines were the same, but the Campbellites DEMANDED the Irish version convert to CofC and follow “their” teachings, and be rebaptized.
***if any one followed the biblical teaching of salvation***
Dot the i, cross the t OUR WAY or else. Been there seen that.