I can assure you most strongly that they do, on a great many subjects!
Which is probably one of the reasons why there are parents (religious or otherwise) who may not feel comfortable with what the State is teaching in a sex education class - because the focus of the State on supporting the needs of a diverse group of children will be somewhat different from the focus of parents to support the individual needs of their own children.
I personally view the State's role in this as not doing much more than giving kids the minimum information they need to counteract the negative physical implications of sex which causes a drain on State resources - e.g. pregnancy, STIs - which is why I think watching abortion videos is useful - and also the State's role should be to counteract bullying in order that people can get on together in a public space.
I think it is the State's role to put in place mechanisms in a school to minimise bullying of children, and if the only way to do that means teaching kids values about equality that contradicts the values of their parents, then so be it. In a public arena I think the State has the right to require people to adhere to standards that enable friendly interaction. If the parents don't like the protective role taken by the State, they are free to home-school their kids.
ETA: Or parents can lobby for change and see how persuasive the school, other parents and the governors find their arguments. I believe some schools withdrew a sex education video aimed at primary school kids, showing an animation of 2 people having sex, after pressure from parents that it was too explicit.