We live in a society that is thoroughly saturated with religious indoctrination. You can't protect or prepare your children for that by hiding it from them, and you're unlikely to succeed at it if you try. That stuff about God providing courage, direction and comfort? They're going to hear that whether you let them watch Veggie Tales or not. Better to have it out in the open and put it in the same category as Santa Clause. Something that makes a nice fantasy, but isn't real even though they may encounter some who believe it.
You can't compare Santa Claus, to what Veggie Tales does. For one, Santa Claus is recognizable to Christmas (not necessarily Christianity), I have seen many versions of Santa Claus cartoons, read stories etc., and not one of them taught me anything about Jesus or Christianity. Now, Veggie Tales does exactly that (though not so much on the Jesus). It tells you about Biblegod , and things relating to Christianity.
Santa Claus doesn't.
But you're correct in that everyday life, at least in the US, does have indoctrinating effects of one religion over others, that being Christianity. However, it could be compared with the everyday of seeing vehicles, or hearing about Hollywood, or similar things. It has a passing effect where it's not necessarily jammed down your throat as a specific thing would be, like constantly reading what seems to be a neutral book, or watching a single television.
Children tend to watch things they like over and over again. I remember my sister, when she was a child, would constantly watch The Little Mermaid, and in doing so it had an effect on her in her later years (nothing negative).
Positive indoctrination may have a better and more holding effect on a person's mind rather than negative indoctrination.