For those of you that find homes for dogs... (breeders, rescuers, etc)?

At the rescue I'm involved with, we only consider things that would directly influence the potential owner's ability to care for the dog. Most of the things you listed are personal choices, and generally wouldn't affect having a dog, except having adopted kids, only because that's just the same to me as having kids, which is a potential concern depending on which dog they were adopting. The age of the kids is also a concern as well, only because some dogs don't do well with kids overall. If someone had babies I would not consider adopting out to them because the dog and baby would be battling for attention (and baby always wins).