My, relatively recent, experience of faith schools (both daughters attended them) is that they do accept pupils from other faiths, and RE, compulsory to GCSE level, is more about morality than the specific faith.
That is a change from my school days in the 50's and 60's when RE was primarily about the particular faith of the school, but was not a compulsory GCE subject. that bias towards the faith of the school in RE teaching was changing towards the end of the 60's when I left school.
With regard to NI, I had a gratuity aunt who was born there and she used to tell me a bit about what it was like there in the 30's - walk on the wrong side of the street and you risked getting beaten up sort of thing. That was in one of the cities (Belfast I think).
The NI people I knew when I was at college were making similar claims in the early 70's, but never had any problem mixing with people of all faiths over here.
The only NI born person I knew over here who was really anti-Catholic was a Protestant. He wouldn't even speak to someone he knew was a Catholic, but still married a woman who was brought up as a Catholic, though lapsed. When they moved to NI some years ago, they went to move to area where there wasn't a sectarian divide, or where such bias was minimal.
So, though I don't know NI, I suspect that the sectarian divide is strongest in major towns and cities. That would be down to the "them" and "us" attitudes that parents teach their children, having been taught it themselves from experience and their own parents.
Giving children the chance to see that children from the "other" side are just like them really when it come to the important things is a good idea. It will take time, but given enough of it there is at least the possibility that both sides will eventually be able to get on without all the divisiveness which has been seen in the past.
Over here I don't think faith schools are divisive because, outside of school, children mix without worrying about what faith their friends are. They come across people of different faiths daily, they are taught about other faiths in RE, and most of them don't give a hoot about what faith their friends are or about the faith of their parents.