@KatySun
many non-denominational schools in Scotland are partnered with the Church of Scotland though in so far as the pupils go to Church of Scotland churches for services and the minister visits the school for religious observance which is a statutory requirement - or has that changed recently? I really don’t think they are completely non-denominational.
The small town I lived in had 2 Church of Scotland churches and a Scottish Episcopalian Church. Their ministers took turn about to deliver a short talk at weekly assembly. The school attended a Christmas, but not an Easter service at one of the 2 Church of Scotland churchs each year (the Episcopalian Church was too small)
I don't honestly know if my son's school had visiting ministers- I don't recall him mentioning it. They also only attended a church for a Christmas service.
Someone asked about sectarianism- I honestly don't know how big a thing it is now. My family were northeast (very lapsed) Catholics (i.e. Catholics who never converted rather than of Irish background). I honestly had no idea what my husband (Glaswegian) was on about when he talked about Sectarianism as it's a Glasgow/West coast thing.
There are Catholic schools in Scotland but they are very much a minority but beyond that there are no church schools. Scotland doesn't have anything the set up of parents having to pretend to be religious to get their children into a good school as seems to be commonplace in England.
I have been an atheist from around age 7 when it struck me, in an RE, class, that I didn't find it believable. I don't recall however finding the RE/school assemblies at all oppressive or preaching. My recollection is it was done with a pretty light touch and an emphasis on kindness. That was mid 60s to late 70s. That's the same approach my son's school took, but he was also taught about other faiths and what they believed.