Boogers
Tbh I think you are exaggerating somewhat.
Many many threads turn into state vs private but often that is to do with firstly how the thread is titled, where it is posted and how contributors responded to attempts at shite stirring.
I think if you post 'does anyone know if lady Eleanor Holles has a good sporting reputation' in education, you get appropriate replies.
If you post 'should I sell DD to get DS1 a place at Eton because he is quite the brightest boy in the world and I worry about lice at our local state school' you will get your arse kicked.
The other thing i think would help generally is if people tried to
A) respond politely but robustly to arse 'you may think private schools are the devil but that is not the point of this thread and thesis not aibu, you sanctimonious twat'
B) resist the thick as pig shit urge to respond to an attack on private schools by attacking state schools.
C) report persistent offenders for goading.
Loads of sections have this problem. But trying together a section on private schools is a horrible idea imho