[I]t's odd how when politics enters the picture, people sometimes acquire a faith in the Svengali-like powers of teachers that makes absolutely no sense at all. In normal life, we know that overbearing or biassed (sic) teachers are more likely to annoy their students than anything else, and that even good teachers are not always believed. In politics, people sometimes assume that normal, obstreperous kids and adolescents are somehow transformed into docile, sheeplike (sic) beings who accept every word their teachers say. As a teacher, I find this very selective faith in us and our awesome powers quite perplexing.Amen. There is a lot to be said on the topic of how political figures shaft the teaching profession on a regular basis (it's the educational equivalent of the player/manager dynamic, teachers fail and pupils succeed, unless its during an exam period, in which case the exams have been dumbed-down because we all know they used to be harder), but this isn't quite what Hilzoy is getting at, so I'll put away that particular soap box for another time. This about parents being terrified that the philosophy and morality of a school teacher will somehow trump their own.
Having said that, the two ideas are linked. My first thought upon reading the above was "This is Section 28 again". I've mentioned that particular law before, but if you're late to the party, Section 28 was an attempt by the Conservatives to prevent "promotion" of the homosexual lifestyle in schools. It was feared then, as now, that if teachers spent their time discussing homosexuality with their classes, children would get the idea that this is "the norm". I suspect that in this case (and I may be entirely wrong) that S28 was a deliberate sop to this particular subset of outrageous parents, rather than a deep-seated aspect of party philosophy.
I guess I've never understood where this attitude comes from. Looking back over my life, I can think of plenty teachers who were incompetent (usually because they either lacked the "killer instinct" necessary to keep a class under control, or because they were so relentlessly unpleasant that all higher brain processes were abandoned the moment they entered a classroom), many who were good at their jobs, and a few who were truly excellent. That latter category describes maybe three or four teachers across one's entire educational lifetime, and even then, their tremendous ability to impart knowledge and inspire interest and dedication is a separate skill-set entirely to persuading children to alter their moral standpoints. And this is coming from someone who tended to be one of the most attentive people in a class (more through fear of punishment than any deep desire to learn, it has to be said), and whose slowly crumbling faith in God meant I was already searching around for alternative philosophies. Hilzoy is quite right that proselytising teachers are going to be annoying rather than persuasive, and it's worth noting that it's hard enough to get children to accept facts  let alone your personal opinion on something.
What might just happen, if you're very lucky, is that once in a blue moon you'll find yourself in a conversation with a small group of children who are in the right frame of mind to ask and answer sensible questions, and aren't being expected to be doing something else right at that minute . Outside of the "citizenship" sessions we had for twenty minutes a week (which to be fair did occasionally generate some good discussions), I remember pulling off this trick all of once, when I got to have a short conversation on whether homosexual couples should be allowed to adopt (given my opinions on such, S28 would have prevented that conversation had it still been in effect).
This, apparently, is what has people so frightened. From time to time a conversation may arise in which it becomes clear that a child's teacher feels differently on a given subject to their parents. The idea that a brief chat about such things will invalidate years of whatever philosophical indoctrination these parents have engaged in (and of course many and perhaps all of those claiming outrage will have had their church or whatever knocking this stuff into their kids' heads as well) is ludicrous. If it was that easy, no-one who went to a religiously-affiliated school would ever lose their faith (we'll bypass the self-evident truth that even sending your children to, say, a Catholic school, does not mean that Catholic parents will never disagree with anything discussed in class). Moreover, the idea that faith in one's dogma can be so easily overturned is both somewhat insulting to the pupils in question , and, if true, would mean the downfall of organised religion almost immediately, since preventing your children (or your flock) from ever being exposed to counter-arguments is manifestly impossible, unless you choose to seal yourself away and never have contact with the non-believers. Which is a viable choice, but be honest about it, don't send your child to school with everyone else and then complain when different opinions get raised.
I guess in conclusion I'd say that Hilzoy is right that people seem to have a funny idea of the level of influence teachers have, and that it's a wider problem than just on the subject of politics; parents often have a truly bizarre concept of the role, responsibilities, and effect we have on their children's development. I'm also continually baffled by the idea that faith is such a fragile thing that it must not be challenged, even indirectly, by coming into contact with other ideas. What a miserable, paranoid existence that must be.
 I once told a class of very bright Year 8 children that it was physically impossible to write down a googolplex (that's a one followed by a googol's worth of zeros, i.e. 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 zeros, in case you were wondering). Two weeks later I discovered that every time I hadn't been looking one of my pupils had been trying to write said number in the back of his maths book, so as to prove me wrong.
 I realised pretty early in my time teaching that kids had worked out they could avoid doing any work if they asked me a question I found interesting enough to answer in full; from then on I let them get away with it assuming I thought the question was more important than, say, five extra minutes of practising balancing equations.
 This is an extension to the "exams are getting easier" ..., the idea that children are so fundamentally clueless that they cannot do well unless the bar is lowered for them, and they cannot think critically on their own so must never be asked to defend their positions.