One idea I've been toying with is an America in which Appalachia has a large Catholic population, and like OTL the region is very very poor but the idea is based around activits in the Church combined with lay activists and attempts to unionize faceing resistance from wealthy WASPs mine owners and plantation owners and instead of a region being fractured by racial and religous tensions the Church is used as the glue which binds the union movement, turning the Appalachian region into a hot bed for a poltical party born from the struggle that is a combination of being what is considered traditionally right socially and left economically. This party would compete with the Democrats and Republicans.
Another few ideas I had leading up to the Catholic majority in Appalachia are Catholic Irish and Socts are removed in large numbers and forcefully transported to the North American colonies or move on their own, which ever, and due to the hostility towards Catholics in the Colonies they move into the sparsly populated Appalachian region. The region sees over the next 100 years a steady stream of Catholic immigrants from Ireland, Southern, and Eastern Europe who instead of settling in the cities end up moving into the Appalachian region and the surrounding foothills which already have a large Catholic population. Granted this is really really sketchy and poorly thouhgt but I'm working on it. Another idea was that large numbers of French Catholics somehow end up in the region after a British victory in the French and Indian war (Americas chapter of the 7 Years War).
Another few ideas I was toying with was having a very large Jewish minority in Savannah Georgia, Cossacks in the Dakotas, Muslims in Texas, and a large influx of Chinese into Britsh Columbia (granted its not part of the US but I thought why should Canada get left out of a major demograhpics shift?).