Egg allergies trigger careful treatment protocols surrounding many influenza vaccines, but do not in any way preclude vaccination or exempt one from it. Specifically, if your allergic reaction to eggs is severe enough to impair breathing, delivery of the vaccine must be delivered in a monitored medical setting that can treat you if an allergic reaction that impairs your breathing. You are only precluded from receiving an egg-based vaccination once you have experienced a severe reaction from an egg-based vaccine. Egg allergy alone is not sufficient.
But for the vast majority of workplaces, there's not much of an existing precedent to do this, and I suspect the vast majority of employers will not want to rock the boat too much. I suspect it'll be something that will be "required" by policies but not enforced in practice. The people who want to get vaccines will get them, and those who do not will ignore the policy without repercussions.
That would seem to be extremely unethical and possibly at least borderline an OSHA violation. If a workplace is claiming that certain procedures are being followed and they are in fact not being followed, I think plenty of lawyers would be happy to take that lawsuit.
As far as this being unethical -- maybe it is -- but since when has that stopped anyone? There are people still being forced to go to work sick because they have no way to take sick leave without losing their jobs.
At the end of the day, it's a lot less risk to HR to not piss off a couple of politically fringe employees over something that the vast majority of employees will do voluntarily anyway, without any coercing. Two unvaccinated employees out of hundreds probably won't cause a problematic COVID outbreak, but they could file a lawsuit.
I'm also not sure there's quite the bright line you seem to be suggesting between "at risk" and "not at risk." Young health people still die of COVID-19, just not at as high a rate as already-unhealthy or older people.