Not that talking sense often stops panic, but you might remind those panicing about the birdflu that when the Black Plague hit, stray and pet cats were killed to prevent the spread and ALMOST CERTAINLY THIS MADE THE SPREAD WORSE!!!!!

Strays kill the sick birds, preventing them from spreading the disease, just as cats killed the rats that harbored the infected fleas. Yes, cats may get the disease (though they may well not die of it as each species reacts differently) but they very well could prevent the disease from spreading to the poultry farms as they presumeably will not fly over the fences and share food leave droppings to infect the flocks as infected crows or sparrows easily could...unless some predator (like a cat!) killed the sick bird and kept it from going for an easy food source.

Hope this logic gives you some arguement that they can understand.... like the stray cat may just be SAVING them MONEY and perhaps their lives.