Yesterday, the EEOC published its guidance on the COVID-19 vaccine under the ADA and GINA, in the form of nine Q & As. You can read them in their totality here.
The TL;DR: yes, you can force employees to receive the COVID-19 vaccine as a condition of employment (although the should is an entirely different issue), subject to limits on reasonable accommodations for employees' disabilities and sincerely held religious practices or beliefs and subject to limits on pre-vaccination medical questions.
That's more or less aligned with everyone's collective conventional wisdom on this issue. What is new in this guidance is the agency's position on what to do with employees who refuse the vaccine for medical or religious reasons.
Sincerely held religious practices or beliefs present a different problem for employees since Title VII does not offer a similar direct threat defense to an accommodation request. According to the EEOC, "If an employee cannot get vaccinated for COVID-19 because of a disability or sincerely held religious belief, practice, or observance, and there is no reasonable accommodation possible, then it would be lawful for the employer to exclude the employee from the workplace." As is the case under the ADA, however, this lawful exclusion does not necessarily equate to termination, and alternative accommodations should be considered.
The bottom line for employers? The COVID-19 vaccine is here and will be available within months for your employees. Now is the time to figure out how you will handle it for your employees. Will you require it or recommend it? Will you offer it on-site or send employees elsewhere for the vaccine? What will you do when an employee objects for medical or religious reasons? Planning is everything, and with an issue this important there is no reason to be caught unprepared.