At least I know the Red Cross is doing better at sheltering people with disabilities. The overall training for sheltering people with disabilities is pretty good, and everyone should know how to deal with service animals. Any shelter I'm associated with is going to make sure everyone is taken care of.
I had a tough situation the other night, a fire victim with fairly severe MS. He was out of his apartment until power and water damage could be repaired, and his family could not put him up or assist with his care (ex. stay in his hotel room). We couldn't just put him in a motel, he needed ongoing assistance. And an ER would just evaluate and release him. We were lucky, and found a temporary spot in an assisted living facility, and it was a good place - I would have put my father there. It took less than 3 hours late on a saturday night, and I had to think how many weeks we looked for a bed for my Dad. Like another thread pointed out, sometimes the difference between home and homeless is pretty thin.