I dislike this definition that gets thrown around a lot. There is an important distinction between rejecting/absence of the belief in a God and believing there is no God. The latter is fine in everyday chat but if you're trying to have a genuine debate with some it's just logically incoherent and should be interpreted as lacking a belief in a God.
Heh. The key difference is facts. The science teacher should be teaching facts. I have no problem with a science teacher teaching facts because these facts don't interfere with my world view. If you mean that they shouldn't be telling students that this proves that God doesn't exist or is therefore unlikely (i.e sharing their atheist-minded conclusions) then I agree. Much like I'd expect a religious science teacher to stick to the facts and not sneak in a "but this doesn't exclude God, children!" or a "... which was all thanks to God!".
People get uneasy when religions request equal footing because religion is not on equal footing with Science in a fact-based learning environment. This is something many religious people have trouble accepting.
I don't really understand why if religion is such a personal/spiritual topic that it can't be taught in the home by family or at Church. That being said, elective religious classes don't bother me too much, as long as it's not core/compulsory.
How does one even teach secularism? The point of secularism is to be free from religious based rulings and teachings. When religious subjects are only elective and not compulsory, I'd argue you've achieved a reasonable level of secularism. Don't get me wrong, I'd totally be in favour of complete separation, but surely this is a decent middle-ground.