Should I just steal someone's neglected cat?
Why do you want to steal their cat?
I'll call local shelters and try to find a home for it
I think that you should leave the neighbor cat alone. It is not nice to try to take an animal that does not belong to you.
Alright, if people don't want their cats anymore, I'll take care of it for them.
If that cat is being neglected by its owner you should call proper authorities on them. You'll get in trouble if you just stole it. Your intentions are well but there is a better way to deal with the situation.