Can the government dictate the ‘look’ of the people we prefer to hire?

Q. We are a retail company. Our public image and our reputation for being a patriotic corporate citizen are both very important to us. We tend to hire a predominately young workforce and individuals with trendy, but “clean cut” and energetic appearances. I also don’t want to be forced to hire people with head coverings or facial hair, which we don’t allow. Can the government force us to do that?