Perfectly fine.

Employers can set standards for employment. Dress codes, fraternization, morals clauses, certain numbers of days absent, living in the school district, etc. As long as it doesn't violate discrimination based on race, religion, sex, sexual orientation, or handicap (did I leave any out?) your employer has every right to establish the workplace they choose.

Having a armadillo tattooed on your forehead is not a protected class.