Re: Employment
It depends entirely on what the laws are where you live. There's no federal law that prevents this kind of discrimination, but state and local laws vary. I've lived in cities that did have laws prohibiting such discrimination. In one case that made the news, an applicant for a parking-garage attendant position was offered the job but was told he would have to shave his beard. He filed a complaint with the local authorities and won. The company was headquartered in another city and didn't know the local laws. Oops.
The law in my state doesn't specifically prohibit discrimination based on appearance, and it does say you can discriminate if there is a bona fide occupational need. For example, it seems to me someone could be required to shave a beard if he had to wear a respirator and couldn't get a proper seal unless he was clean-shaven.
These kinds of laws are usually anything but clear-cut, and there are several protected classes (e.g., suppose a Sikh applied for the apprenticeship; their religion forbids them from cutting their hair or shaving their beards).
This is the kind of thing only a competent lawyer can answer, so don't take my information as definitive.