Employers may legally impose grooming policies. How they implement the policy may depend on a variety of considerations, such as the length of the hair, the nature of the job the employee does, the customer they serve, etc. What they cannot do is treat people differently because of race, nationality, or some other improper consideration. You do not provide any information that would indicate unlawful discrimination other than that other employees have some form of facial hair. Have you asked why you have to shave and not other men? Was an explanation offered? More information is needed before anyone can form an opinion whether making you shave violates any right you may have.
They say you get what you pay for, and this response is free, so take it for what it is worth. This is my opinion based on very limited information. My opinion should not be taken as legal advice. For true advice, we would require a confidential consultation where I would ask you questions and get your complete story. This is a public forum, so remember, nothing here is confidential. Nor am I your attorney. I do not know who you are and you have not hired me to provide any legal service. To do so would require us to meet and sign written retainer agreement. My responses are intended for general information only.
Your manager doesn't seem to be exhibiting good leadership. If the rule is being applied inconsistently, then he should be able to tell you why. However, as a general rule, bad leadership is not illegal, except for the situations that Mr. Kirschbaum aptly described. Good luck.
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