I have just seen this thread and felt I had to add my experience of adopting 3 young cats from CHAT Lewisham - 2 siblings, then later a 2nd cat, so two sets of procedures so to speak.
I live close to a busy main road, I live in a working class, non affluent area and have up to 6, yes 6 children, all but one aged 0-5 in my home on a daily basis - I work as a childminder.
Lesley, the rehoming lady came out to see me on a day I was working, so she could see the set up and match us with appropriate cats. Before she even rang my doorbell, unbeknowns to me (until she told me in discussion) she had walked around the neighbourhood and looked at the busy road, checked the buildings nearby (we have offices and industrial units nearby) . She then came in, and after a good chat about our wishes and what we could offer a CHAT cat, I showed her around my home. We talked about if the cats had escape routes from over zealous toddlers, and how to introduce them to the garden space.
Lesley and I then sat back down and she told me that she thought an all black cat would not be suited to our home (my daughter had asked for one as she heard they we often overlooked) as if they did get out, they were more likely to be run over on busy road. We agreed cats 6months + would suit us as they would be more confident around the children. We also agreed the cats would only be let outdoors via the back garden which, as catneuterer described, meant they had back to back gardens to play in.
At no time did I feel patronised or limited by this discussion. It was very friendly and I was pleased that we were getting cats at all. It was a mutually positive exchange. Lesley knew her cats and I knew our household 
I am surprised that people think CHAT are picky, as I had prior to this exchange, experienced resistance to adoption of cats to those with children from two large ,local animal charities, and this experience was repeated by a friend a year later.
I have nothing but praise for the work they do, One of my original cats became unwell and died suddenly, there was speculation about inherited problems and CHAT went out of their way to check this out, and take extra care of my other cat, when he went for a routine procedure, as they knew I was concerned. They were also very supportive when my other cat went missing, earlier this year.