Yes. Many employers are worried that piercings or tattoos will offend customers and they are allowed to tell you to cover your body art.
In Cloutier v. Costco, an employee who claimed her eyebrow piercing was part of her religious observance as a member of the Church of Body Modification, and objected to Costco's dress code policy after she was fired for refusing to remove her eyebrow piercing, had her legal claim rejected. The court ruled that the accommodation requested by the employee - to be exempt from the policy - would be an undue hardship on Costco, as it would adversely affect the company's public image and would detract from the neat, clean and professional image it wishes its employees to portray.
Based on this ruling, it will be very difficult for those who want to bring legal challenges to succeed, especially if the basis for their choice to be pierced is not a religious one.