No - the company has the right to require literally anything as a condition of employment - and you have the right to quit for literally any reason
Discussion
In a free market that might work. But as governments subsidize large corporations and strangle competitors, we end up with a corporatist (socialist) structure where employees have few options but to go along with government dictates.
The solution is freeing the market so that competition and options can exist.
Although I acknowledge that one root problem is the power of governments to scare companies toward mandating vaccines and masks. Without that pressure, companies would have little incentive to harass employees with irrational and intrusive mandates.