Any of those homes not taking in these people are hypocrits of the highest order and should be called out.
This sounds like a good project for someone who wants to start their own little Project Veritas type group.
They should go undercover as a member of some organization trying to link illegals to people with extra rooms and ring the doorbells of this home and film the response to something like, “We know from your sign you must be a supporter of Governor Whatsherface and have heard her calls for help to house homeless illegals, so we are here to help you get this process started.”