Honestly, OP, I find the RC schools a lot more chilled about religion.
Possibly because they don't get charismatic/Evangelical Church members trying to stop the teaching of Science, particularly evolution, and getting upset about such 'demonic' and 'purely Satanic' things as the Catholic celebrations of Dia de Muertos being used as inspiration for art units, any mention of Halloween/All Hallows' Eve/All Saints Day, etc.
RC ones don't demand all students take part in Communion (but CofE ones in my experience, are enraged if anybody refuses Eucharist or doesn't attend optional services) - for example, it was compulsory for staff to participate at one CofE school's eucharist, passing the wafers and grape juice, even though, by their own rules, the staff members were excluded from participating because they didn't recognise the particular denomination - it was demanded that all staff pretended to be CofE. At the RC ones, You aren't Catholic/in good standing within the Catholic Church? Meh, are you OK with coming along to help supervise, then? In a similar vein, one of my old places had a requirement that anybody responsible for the spiritual welfare of the students (form tutors, pastoral staff, etc) had to be a practising member of a Church. The RC one? Don't care, we just want the best staff we can get.
The only 'more religious' bit seems to be the crucifix:room ratio being higher. And the chapel is in far better nick.