Yes. But, 99.9% of companies don't need or require that. We live in a market where we pay millions of dollars to men to run into each other while wearing equipment. That's almost the same thing. A coach should be able to fire someone who doesn't want to go across the linebackers. Someone will want that job, and replace the fired receiver.
I think you are out of touch with reality.
Try branding: should a company be able brand its employees and fire those that don’t accept it. (Assume a new policy and a long operating company.)
No way- they would be sued out of existence. Rightfully so.