The C of E really is pretty harmless.
My older daughter is in her first year at the local C of E secondary school, younger one will go there in 18 months.
Excellent school, just got an “Outstanding” OFSTED report, 10 mins walk away – what’s not to like?
The school is church funded (and regular church attendance for at least 4 years prior is a prerequisite of entry) and, in year 7 at least, there is quite a religious angle underpinning a fair bit of what they do. However, I don’t think it’s intrusive or worrying, and it’s a fair price to pay for my kids getting a very good education for free.
Frankly, if a kid is overly swayed by religious teaching at school I’d say it’s more a reflection of the parenting they’ve received (not aimed at the OP). My kids are level headed and form their own opinions on things – their take on religion (bearing in mind they’ve gone to church for years) is much the same as mine and my wife’s – rather bemusing, interesting from a historical perspective, and just something that’s out there, nothing to get too bothered about.