I think there are, at least, a couple of things, here:
It's not about asking in order to make accommodations for those who are medically unable to get the vaccine, it's about asking in order to dispense with the services of those who are unvaccinated. If it was just about asking in order to accommodate everyone currently employed (as we're potentially talking about dismissing people for being unvaccinated) then that might be a different argument.
On the negligence angle, I'd have thought that it's about the assessment of the level of risk to others, i.e. what level of 'endangerment' there is and how serious the potential effects might be. If the vaccines prevented catching the virus and the transmission of it (rather than mostly reducing the likelihood of developing a serious condition oneself as well as helping to reduce transmission - by an uncertain amount) then I think there would be a stronger case for talking about gross negligence but this isn't the case, is it? Also, one needs to factor in the demographic of the average workforce and thus the inherently lower risk profile, no?
IANAL (obvs, too)