Most states have what is called "employment at will", meaning that you can be fired for any reason as long as it isn't expressly prohibited by law. Different if you're covered by a union contract. But other than that, that's the general rule.
So, there is a specific law saying that you can't be fired for refusing to have sex with your boss. There isn't a specific law saying you can't be fired
Let me try it this way.
The Federal Government has no authority to use OSHA, or regulatory authority, to pressure companies into doing this.
Such power is given only to the individual states.
And — requiring someone to take a treatment that is under Emergency Use Authorization is prohibited; the Dementia Joe cabal said months ago they won’t be enforcing that prohibition until May of 2022.
And — the Emergency Use Authorization cannot require you to take the jab, if you belong to a group which was excluded on Medical grounds from participating in the trials (including the obese (BMI > 30) and those with high blood pressure, and pregnant women.
Trying to make someone take a non-authorized treatment, and discriminating against them on the basis of a health condition, IS a Constitutional violation.