I first started supporting Liverpool as a young kid in the 60s but really started following (ie attending games) in the 70s. In my experience, though Liverpool has been said to be the Protestant club in the city, I dont really think religious polarisation has really shown itself.
There are loads of Liverpool fans with affinity to Celtic and loads with affinity to Rangers and in my experience its been a very friendly affair. If you have ever listened to the Twelfth Man CD of Liverpool songs that has been for sale outside the ground there is a short track with two sections Liverpool fans (I think in the Albert) chanting Rangers- Celtic at each other for a short period and then breaking out into other chants. All very friendly, so it seems.
Liverpool is a very tolerant city, unless you are a Tory politiican. I think only Cardiff comes close, from what I have found. Liverpool generally accepts all races, creeds and beliefs and I can honestly say that the religious divide that is said to plague Belfast, Glasgow and Edinburgh in respect to Glentoran/Linfield, Rangers/Celtic and Hearts/Hibs has not been seen by me in forty years of match going.