The answer to this question, in nearly all if not in all instances, is yes. Employers may require their employees to get COVID vaccinations as a term and condition of maintaining their employment. It is conceivable (conceivable not being the same as likely or even possible) that there could be some small, small exceptions to this rule.

Some have claimed that employees may object to COVID vaccinations on religious grounds; in other words, that getting the COVID vaccination is contrary to their religious beliefs and practices. While it is true that both federal and Kentucky state law prohibit discrimination on account of religion in the employment context, an employer is required only to accommodate reasonably an employee's religious practices, and it would seem much the better argument that this duty does not extend to allowing an employee to go unvaccinated and thus pose danger to other employees and customers etc. A federal judge in Houston, as the New York Times reports this date, has dismissed a lawsuit by employees at a hospital there challenging their employer's requirement that they get a COVID vaccination, A Judge Dismisses Houston Hospital Workers' Lawsuit About Vaccine Mandates.