I initially thought so too but I have found that sceptics and supporters can be members of both sides of the religious divide.
A prime example of what you are saying is Brenda Leyland who if not a catholic was educated at a catholic college
In the west of Scotland where I live sectarianism is a fact of life although thankfully not nearly the all pervasive thing it once was but I think I recognise many of the hidden traits
* in some of the internet posting I have seen.
*For example I have had sight of employment documentation from a shipyard stating "Catholics need not apply" an open secret at the time I think. But somewhere out there is a man who came from primary education as a wee boy into the 'big' school accompanied and labelled by a record, unbeknown to him or his parents, that "This boy shows anti social tendencies - plays with Catholics" . Thank goodness for computerised records and transparency now but I often wonder if that boy suffered from that evaluation.
So maybe my thinking on this is entirely down to me rather than to anything else; it is interesting though that you initially thought along those lines too, as I believe you are also very familiar with my part of the world.