First of all, paying for a badge will in no way affect your status as an exempt employee. Secondly, an employer can require that an employee pay for lost or damaged equipment, which your badge would be considered to be. Accordingly if you don't pay, then your employer can refuse to give you a new badge. The fact is that most work is "at will" which means that a company can set the conditions of employment much as it sees fit absent some form of actionable discrimination or action breach of the terms of a union agreement or employment contract.