While you've brought up perfectly valid points, you didn't actually refute anything I said.
Yes, some people are required to shave for their job, but most are not and still do. Some women are required to wear makeup for their jobs, but most aren't and still do.
Regardless, my initial arguments still apply to all the cases where one is not required by one's job.
facial hair can be a potential fire hazard, and is often considered to be too unhygienic for food workers. Both are reasons for an employer to request your continual shaving.
Do similar problems arise for cosmetics and the people that wear them? I don't wear cosmetics, but I don't believe that there are any overlapping laws which restrict their use such as the rules that food handlers must abide by.