PSHE is a somewhat skewered example. Its subject matter has been a political football for years and I strongly suspect the governors & busybodies have had a greater say in it than many others. Their duty is to protect the interests of the school and that must partly overlap with ensuring the school is on the right political wavelength - And the present political position is to not offend anyone at all costs. Homosexuality unfortunately
offends religious people. And we all know what a big deal that is. Hence, very little discussion in schools, even in an increasingly liberal society like the UK.
It's what happens when politicians interfere in institutions which should be subject to no outside agendas.
For example, I believe Tring's admissions policy is favourable to those who can show they attend church
It is. 10 people a year when I applied. Since I was out-of-county my application was through the Church (I live in Bucks but Tring is in Herts).
10 out of a year of 250 is not significant, but it is hardly insignificant.
I recall signing condolence books for the two students who died during my tenure. In particular the book for Josh Brand, who was probably more atheistic than I am! It was notable just how many people wrote something religious or spiritual regarding heaven or the afterlife. The high proportion of such messages did lead me to re-assess the impact of the selection process, both formal (school stipulation and informal (parental choice) Maybe that's just my bullshit detector skewing my views, I dunno. Or maybe atheists just don't sign condolence books as much as religious people?
Like I said, after attending 2 faith schools for my whole childhood, I have come out a radical atheist

It depends on the extent to which the faith influences the teaching and selection processes. I think, for once, the Lib Dems have the right idea: Link state funding to the number of non-religious students and allow students to opt-out of any religious assemblies and activities. Remove the right to stipulate religious belief among all staff except those teaching RE. Scrap the bloated national curriculum and replace it with a much more basic, simplified outline of what was expected. Slash infant class sizes to around 10-15 kids throughout primary schools as far as practically possible.
I'm not sure I understand what you mean by linking state funding to non religious students. And also; no student should ever be given the option to 'opt-out' of anything!!

Always turn it on it's head!! Make religious activities 'voluntary', not all-inclusive.
I don't know much about the plans for re-structuring the National Curriculum - but, largely after watching QI, I do wish we were taught the subject properly the first time around!! Why do some elements of science & history in particular need to be dumbed down to the point of falsehood for the majority of Key Stage learning?
My proposal is that more school hours be devoted to watching David Attenborough & QI. Which party supports that?