Can a person be completely objective in their judgments?

Absolute objectivity really is a myth, and you picked up on that correctly. Even when you deliberately try to be impartial, your brain has already filtered information through your experience and beliefs before you're even aware you're making a judgment. The realistic goal isn't objectivity, but awareness: understanding your own biases and at least trying to compensate for them, listening to opposing viewpoints, checking facts. That's what actually makes sense.