Unless a business is privately held is its PRIMARY obligation to its shareholders or to its customers? What about its employees?

Businesses only have an obligation to the law and to their owners. Whether it's owned by shareholders or a private owner makes no difference. Property rights still apply in any case.

They have no obligation to customers or employees outside of what is mandated by law. Though naturally there is an incentive to treat customers and employees well in order to be competitive in the market.