"Yes, absent special circumstances," I believe is the answer, at least under New Hampshire law. New Hampshire is an at-will employment State, meaning that an employee's employment can generally end at any time for any reason, subject to certain exceptions. The "wrongful discharge" claim would be the exception potentially applicable to an employee who refuses an employer's demand to get vaccinated and is fired as a result. An employee claiming a wrongful discharge must prove a 2-part test: 1.) that the employer fired the employee out of bad faith, malice or retaliation; and 2.) that the employer fired the employee because the employee performed acts encouraged by public policy or because the employee refused to perform acts discouraged by public policy.
Wrongful discharge cases usually turn on whether the employee can satisfy the second prong of the test. In most cases, an employee who refuses to get vaccinated will not be able to show that public policy discouraged him from getting vaccinated. In fact, the converse is true. The public interest favors everyone getting vaccinated so that the death toll stops rising, the hospitals are no longer overrun, and the risk of contracting a deadly virus no longer inhibits the function of society.
"What about a person's right to have control over his own body?" some may ask. This is a private interest, not a public one, under these circumstances--and thus cannot support the public policy prong of the wrongful discharge test. No public policy is implicated by an employee refusing to get vaccinated, simply because the employee is a contrarian or has an unreasoning fear of vaccines. As such, employees of private employers who refuse employer demands to get vaccinated, and lose their jobs as a result, are unlikely to have legal recourse, absent special circumstances.
What might such special circumstances be? An employee allergic to ingredients in the vaccine who opposes an employer demand to get vaccinated and gets fired nonetheless might have a claim. Public policy discourages people with allergies from being forced to suffer exposure to their allergens.
Of course, the courts haven't faced this issue yet and likely will not do so until 2022 or later.
If you have questions about your rights under employment laws, you should consult an experienced employee rights attorney such as Benjamin King of Douglas, Leonard & Garvey, P.C. Attorney King has been ranked in the top 5% of lawyers in New England representing employees in employment discrimination cases, continuously since 2014. Attorney King can be reached at 1-800-240-1988 or fill out our online contact form.