They don't want the shot. They don't want colleagues to know.

“If you’re going to treat vaccinated and unvaccinated employees differently, it needs to have a well-reasoned basis and not be done in a sort of harsh and derogatory way,” said Todd Logsdon, an employment attorney in Louisville, Ky., who is co-chairman of his firm’s workplace safety practice group. From a non-legal standpoint, he added, “the fact that you have some real morale issues — yeah, that employee is going to feel left out so you may have more turnover.”

But unvaccinated workers like Mr. Taranto fear that any company policy that identifies them is like a scarlet letter on their chests.

“My big comment to my boss is this is kind of like a big visual marker of the kind of belief I have,” Mr. Taranto said. “I don’t want this stuff broadcasted out to the world.”