If I were working in this animal clinic that had these rules, I'd probably look for another place to work. My reason is that this boss sounds like a nut job. If they make irrational decisions in one case, they'll probably make them in others, and therefore I could not really trust them. But, while still working there I would honor the rules of the place since its their business and their purgative to come up with whatever wacky policies they want.
Was any rationale given for the policy change? It would be a little different if they had a valid basis for the decision that was shared with the employees to help them understand why the working environment was changed. If it was just blasted out with "follow the new rule or quit", I would find that to be a pretty draconian way to manage... again a reason I wouldn't want to work for this person. Have you asked them why they put this rule into place? You said no one has been abusing a smartwatch at work, so why change a rule. There is always a reason.
Was any rationale given for the policy change? It would be a little different if they had a valid basis for the decision that was shared with the employees to help them understand why the working environment was changed. If it was just blasted out with "follow the new rule or quit", I would find that to be a pretty draconian way to manage... again a reason I wouldn't want to work for this person. Have you asked them why they put this rule into place? You said no one has been abusing a smartwatch at work, so why change a rule. There is always a reason.