A company can certainly require employees to sign policies affecting their rights outside of the company, such as requiring them to not post photos of company uniforms (or the workplace), not discuss business matters in any way, not invest in certain ways (common in the securities industry), setting certain grooming standards (e.g. no beards), etc. Remember, that unless you have a contract guaranteeing your employment, employment is "employment at will"--the company may terminate your employment at essentially any time, for any reason. Therefore, if you don't comply with company policy, the company may fire you. So companies may reach very far into your life, and the choice is to not work there.