You don't have to renounce your passport. Your passport isn't you. The "person" of your passport is one of your persons. This person isn't you, because you breathe and have flesh and bones; it doesn't. The person of your passport is a tiny representation of you. It isn't you.
Doesn't matter much. If you don't renounce your passport, then the IRS will come after you and take away all your savings. Why risk that, when you can renounce your citizenship in a matter of few days?