A similar case already has transpired through the Supreme Court from a policeman ruling in favor of religious facial hair being acceptable. There was an interview with the former detective/policeman on the Deen Show.
Joseph is right. There is a Supreme Court case involving Muslims wearing beards on the job. In 1999 the high court ruled that Shakoor Mustafa and Faruq Abdul-Aziz, two veteran Newark, N.J. police officers, could wear their beards on the job.
There is a major caveat to this ruling being used as precedent for Omar's case, however: The Mustafa/Abdul-Aziz-case involved a publicly funded police force, while Omar's involves a private security company.
At any rate, here's the post-ruling interview that Joseph mentioned in his comment.