To some degree they rely on traditions. In many other ways not so much. But in many ways ALL my pastors are far less traditional than how Book was portrayed. That said yeah it was vague, but not very.
But your pastors would (I am guessing) be in the Protestant tradition? That's a rather broad encompassing thing, granted, but it's been around since the Reformation. The absence of celibacy is more or less uniform, IIRC - it's chiefly practiced in the Catholic and Orthodox churches.
Ah well. On the other hand, I can forgive Whedon for wanting to avoid theobabble as much as technobabble (if I may steal a neologism from another poster here), but Book isn't as well thought out a character as he could have been. He makes the moral and/or ethical quip in a humourful, likeable way, and off he goes. I almost feel that the stuff about his secret past was simply so he could be given a little more depth later on, and it's manifestly clear that the film had basically no use for the guy at all.