Still, I must thank you for your answers as you've convinced me that there is no reasoning with people who feel as you do. Clearly, no matter how I much I talk about my property rights, the city laws against letting animals run loose, the POA's bylaws against letting animals run loose, the hazards of letting animals run loose, my efforts to be humane rather than lethal or any other bit of logic, all I'll get in return is some emotional inane bluster. Why waste the time?
You have convinced me that the only way I can solve cat problem the irresponsible cat people have forced upon me is to trap them and turn them over to the pound or simply shoot them and put them in the trash. I see now that this way everybody wins. People can let their cats run free as they believe nature intended and I then get rid of the nuisance cats on my property per the city and POA laws. Win-win. Though I'm pissed that my neighbors would force me to do this, I appreciate your showing me that I have no other choice.
Have you tried talking to your neighbor(s) about their cats?