No, it isn't. Employers impose conditions all the time. Thousands of them require drug tests, for instance.
That doesn't mean they're forcing you to take a drug test but you must if you want to work there.
Now, if you were forced to work somewhere and the employer required vaccination you would have a point.
In the case of New Mexico, the employer is the State of New Mexico and they forced their staff to get an experimental treatment that is explicitly not allowed as per the Emergency Use Authorization.