The coming from outside of Manchester and being a rag things is a bit outdated now. Lots of families were moved from inner city Manchester to Wythenshaw and estates in Wilmslow, Knutsford etc in the 70s and they've got loads of longstanding blues and rags. There's more geographic mobility so things are pretty mixed up. Prior to the war it's probably true that City fans were from central and east Manchester and the rags more from the outskirts. Maybe that's still a factor as it does feel like eastern side of the City is predominantly blue. Utd attracted a lot of Irish catholic supporters from the migrant workers in the west of the City and Salford but fortunately religion was never really a factor. I think in the 60s United tried to cash on Irish support by declaring themselves the catholic team in Manchester but fortunately nobody ever really bought it.
What the rags have is hundreds of thousands of dedicated followers with no connection to the City at all (or a very tacit one). The number of Rags I've met in London who have an uncle from Manchester is unbelievable.
I tend to think that in the old days City chose you rather than the other way round. When I became interested in football I was surrounded by Rags and had parents with zero interest in the game. Nevertheless, there was one other blue in my class and that was that and instinctively I preferred the whole concept of City. It turned out later that City had been the family club since it's formation but nobody had ever communicated that to me or told me to support City.