Came across this on Youtube. It's a film showing the community in the St Andrew's Gardens area celebrating the opening of the Catholic Cathedral in Liverpool in 1967. Gives an insight into how homogeneous Irish Catholic working-class neighborhoods were up to this time.
http://www.youtube.com/watch?v=uaBZ-7-Xg8k
My guess is that this area which is close to the Catholic Cathedral would have been an almost 100% Everton supporting community then. After the dispersal of the inner-city population to places like Croxteth and Kirkby footballing affiliations would have become increasingly less influenced by religion or ethnic ancestry. Scotland Rd / Vauxhall is propbably the only remaining Irish Catholic enclave left in the city and it remains overwhelmingly Everton supporting. Likewise in areas like Dingle and Everton where there are still active Orange Lodges there would be very few Everton supporters.
It's only really in these areas that there is any lingering connection between religious and footballing dentities.