True example:Company was purchased by a "corporate raider." They announced that on the day of takeover, the new exec would be escorted into the plant. He was to be greeted by the clean shaven upper level staff, wearing, for men, blue dress shirts with yellow ties. Guess who got sent home immediately? The ones who had refused to shave their beards or moustaches, or wore green shirts or blue ties that morning. Looking for people who would follow the leader, hm?
Yeah, they can force you to shave, IF you want to keep the job. Unless you wear your beard for religious reasons, and can document this, you probably have no EEOC protection issues with your termination, either.
And your chances for unemployment insurance would be fairly slim after your termination, as most of the time, this would not be considered an unreasonable request, especially if it is stated somewhere in company policies or rules. In some food prep places, people can wear hairnets on their beards if they have them, but just coming to work clean shaven every day isn't really an unreasonable requirement in most circumstances.