Now here's some maps of 1960. Let me preface by saying that I'll concede there certainly was more bloc voting amongst Catholics this year for obvious reasons than most, but the only other year you can find any such bloc voting is 1928. JFK is believed to have received around 72% of the Catholic vote. That still leaves some obvious areas where such a swing didn't occur:
Long Island? Staten Island?
Long Island and Staten Island were not as Catholic in 1960 as they are now. (LI was around 33% in 1960 and 50% by 1990.) The exodus of "white ethnics" had started but was still gathering steam. Once in the suburbs, the Catholics slowly became more Republican. This was caused by a number of factors being race based politics, the reaction to Vietnam protesters, a staunchly anti-communist church, the abortion issue and just an incorporation into the existing politics of the area.
Now I concede that there is not any meaningful Catholic vote and the one that did exist was by no means monolithic. Irish tended more Democratic than Germans for instance. Middle Class Catholics were also much more likely to trend toward Republicans. And stretching back it was swayable by candidate.