This is not at all black and white, nor is their definitive guidance for any situation and each needs to be examined as they come up.
Here is what makes sense until there is more definitive guidance:
The employer can require a vaccination, but if any person alleges they have disability related issues that prevent vaccination, have religious objections to vaccination, or indicate any issue or objection that would provide them with protection under one or more employment laws, the company would need to take the appropriate steps as required under the particular law that might protect the person.
For instance, if a person claims he/she has an allergic reaction to vaccines and will not be able to vaccinate, that could fall under disability accommodation and the employer would engage in an “interactive discussion” of accommodations, if any, that would allow the person to do the essential functions of his/her job.
With regard to a religious objection, the employer would engage in a different discussion related to their ability to accommodate the religious aspects of the objection.
There are other potential issues and objections as well, that involve legal protections for employees, but they are based on employment law, not employee whims.
Simply relegating someone to work from home without engaging in the appropriate actions related to the applicable law, could be seen as retaliation for asserting their rights under a specific protective law.
Also, the unintended consequence of allowing someone to work from home without engaging in the appropriate actions as required by law, could encourage some to take advantage of the company and force a remote work situation where the company had no intention of having remote positions.
Of course, allowing someone to work around others and not be vaccinated (assuming vaccination is an option) could open the company to a claim that they failed to maintain a safe workplace as is required under OSHA.