To answer your question: NO, shelters should not take in feral cats if the only option is to euthanize them!
When the city took over operations of the shelter in 2012, we did open admission like it had been run in the past.
By 2013, we had limited our intake of cats to only sick or injured cats, and orphaned kittens, since we were not required by law to take in healthy stray (or owned) cats.
The reason shelters take in trapped cats is they think they have to. You'd have to check with the laws in the jurisdictions you serve to see what the laws are. Nowhere in our city ordinance does it say cats can't be at large (only dogs) so we have no legal obligation to pick them up, just sick or injured cats. We do have a "nuisance" clause in our ordinance, but a cat that is just hanging around is not considered a nuisance, only cats that are actively a danger to the public (attacking people). If you let your cat out and it gets into a fight with another cat, that is on you as the owner since you can prevent that by keeping you cat indoors. Property owners are given tips to discourage cats from coming onto their property.
So the other part of this is that most animal control shelters are taxpayer funded and it is a complete waste of taxpayer dollars to bring in healthy stray cats because it doesn't solve the pet overpopulation problem (as you mentioned) and it cost a lot to impound, house then euthanize cats. That is the way to appeal to the powers that be to stop this futile practice.
We have a local TNR group that we work with. First we find out why the person is calling. Many times they are in a panic because they are seeing the second (or third) litter and feeling overwhelmed, so we let them know that the local TNR group can come out and trap the cats and they will re-release them so they can't reproduce any more. We also explain that if they are seeing healthy stray cats - friendly or feral - they are thriving and the only intervention they need is getting spayed/neutered, and explain the benefits of cats for rodent control. Most people have no problem with this and it helps that the TNR group does not charge. The TNR group will make arrangements to set traps. If there are kittens, it depends on if they are older they would be TNR'd, younger and friendly they go to various shelters for adoption. So maybe you can work something out with the shelters not to take in the cats, but instead refer to your group as an alternative to intake.
As for vets, check with your local large animal vets if you have any, or a mobile vet that would come your way a few times a month. You also might want to do what we had to for a while and that is book appointments with a vet every week for the foreseeable future. Maybe you can find someone that will transport, or at least raise funds to help pay for gas. But the more cats you can get done at a time, the more cost effective it is.
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Tracy Mohr
Animal Services Manager
City of Chico Animal Services
5308945630
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