I can only speak from my limited experience of state grammar in NI.
To the best of my knowledge, in the state sector, church attendance, religious affiliation or lack thereof is not even a thing in terms of admissions. It's the score in the test that determines if you get a place and mostly, that alone.
You could apply for the grammar at the end of the street or one 100 miles away. The score gets you in (or not). Once the grammar school has exhausted its places working down the list of scores then mostly, that's it.
As I say, I can only speak from my limited experience. I haven't read the criteria for every school. There have to be rules for what happens if children are tied on a score etc.
I don't know if it would be described as "super selective"? Don't know the stats. That said, there are always disappointed children and that's really tough. Our local secondaries are very good, but there is still what seems to me to be a divide at age 11.
The process was very stressful for us.