Thanks for understanding your neighbor's position, and being amiable. I have a few friends who spend a lot of time, money, and attachment preparing their yards to attract native birds (whose populations are in decline). Cats coming into their properties definitely bug them, and I understand that too. Most people don't like other people's pets roaming around their yards, no matter the species or their reasons. Rehoming to an outdoor cat friendly environment (ie. barn cat) would probably be the best option, but many do keep their cats in outdoor runs and houses. Some let outdoor cats in for interaction with the family during the day when it is unlikely to cause any accidents, but keep them outside in a run at other times. Concerns would be that some cats are unhappy with this set-up and will howl nonstop. I would not bring a cat who is not using it's litter box to the shelter personally (unless you are sure they would state that your cat does not use his litterbox), and would fully disclose this to any new home. The two types of animals I have seen that lead to abuse from people who might not otherwise abuse animals are animals showing aggression and animals who pee around the house. A lot of cats also stop using their litter box during a stressful event or large change (ie. new baby), but go back to using their box after adjusting, especially if encouraged with methods such as limiting the cat's living quarters to a bathroom or other small, easy to clean area, praising and offering treats every time you see your cat int he box, etc. It sounds like your cat was having a territorial adjustment with the new baby, and he may either be fine indoors now, or possibly be fine in a new home. But, I had a male cat who never would use his box or stop spraying even after trying everything we could think of for years with him. He ended up going to a lady's cat sanctuary for older animals, and seemed to do great there. That said, if you can't re-arrange the yard for him, get him using his box again, or find a good home or facility geared towards a cat with his litter box habits, I would personally consider euthanasia at that point. I just don't see a shelter situation working out happily for him even if he was adopted.
Id take him if I was closer too!
