I don't have a problem with people posting pics of my kids. I guess I would if there was a potentially embarrassing photo (there never has been) and if there was I'd ask them to take it down, but photos of them with their faces painted or at the beach with friends... it just doesn't bother me.
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But I also believe people should respect the parents wishes. I've never been asked to take down a photo of a friend's kid (I only post pics of kids whose parents have fb and post pics of them) but if I was, I would. Or maybe just blur the kid out if that was ok with them and it was otherwise a good pic of mine or someone elses kid. I don't think I get to judge other peoples reasons and I can understand why the issues might bother some people.