However, “legacy” employees never signed any document of employment stating they were required to disclose vaccination status the way you are told you will have provide proof of identity and so on prior to onboardung.
In this situation, you have three groups of employees. Group A doesn't want the vaccine. Group B gets the vaccine but doesn't care whether Group A does or doesn't. Group C gets the vaccine and also doesn't want to work around people in Group A out of concern for their own safety. The company has to choose to accommodate either Group A or Group C. In this case, they chose the latter. Many companies will choose the former. But I don't see what's unfair about this? Group A might have started with the company with the expectation that vaccine status is private. But Group C might have started with the expectation that the company will take measures for their safety should situations change.
Note: I think it's debatable as to how many restrictions we should have in place because of Covid. But there's no denying that many people want to reduce their exposure to the virus and I don't think it's unreasonable for a private company to accommodate that.
Many U.S. states have labor law that cover this. And any company that I have seen do anything similar to this has lost money to both the state and the claimant.
Typically, at least for at-will states, the employer simply terminates you without stating any reason. Very simple for the company and the employee at least gets unemployment pay.