Less than a day after new safety protocols were issued for health-care workers treating Ebola patients, thousands of New York City doctors, nurses, janitors and others who could be exposed to the virus gathered Tuesday for a demonstration of the proper use of head-to-toe protective gear.

The event, a joint project of 1199 SEIU health-care workers’ union and the Greater New York Hospital Association, was held at Jacob K. Javits Convention Center. It came in response to nationwide calls by union leaders, nurses and others for...