They can impose any restrictions they want as long as they comply with your constitutional rights and other state and national laws. Trading your account is not one of them.
Yeah sure... what I do on my own time is none of anyone's business...
You're basically saying the company you work for can impose rules on say what gym you go to? Or whether you play soccer or baseball, or none at all... If I do my trades during my own time , they cannot impose restrictions on that, unless it's against the (insider-trading) law.