Even children should not trust as children; you don't want your son or daughter believing the "nice neighbor" who only want to offer them a piece of candy, an ice-cream or a glass of lemonade in his kitchen, do ya? 9 times out of 10, that IS all he's offering, but you want the kids to come to you first, right, or for the neighbor to ask you first?
My parents made a conscious effort to NOT have us believe in Santa Claus, and I can't remember them pushing religion on us either. They might have told us the age-appropriate stories from the Bible, but they read to us from a lot of different books. I think my Communist brother has some kind of faith; he wears a crucifix on a chain around his neck, at least. I don't know what my sister and other brother believe, it's simply not a subject we discuss among us, it's a private matter.