Many animals, both wild and domesticated, can pass diseases to people. These are zoonotic diseases. Although we should be concerned about such diseases, there are common myths about the public health risks associated with community cats.
Still, those who are charged with protecting the public try to use the excuse that community cats are dangerous to humans. When Trap-Neuter-Vaccinate-Return (TNVR) programs are put into place each cat brought in for spay/neuter is generally given a shot that will protect the cat from many diseases. This makes it safer for humans too.
TNVR is a win-win. The cats win with TNVR because the shots and desexing allow them to live healthier lives. The public wins with this also. When the health department and local officials support TNVR, the public is better protected too because the chance to transmit a disease from cat to human is greatly reduced or eliminated.