This is the correct law on doors. Ive talked to CHP and local police and IF your vehicle comes with doors that are bolted on then they must remain on while driving on public streets. At the moment I dont have a rear bumper on and the police say I must have one on since it came factory with one. This I thought was rather silly but cali laws are very strict. I did ask about half doors and there is nothing in the law preventing them since they are for the most part factory. Even tube doors are not considered legal here.
My buddy runs his tube doors all over the place and he's never been pulled over but maybe he is just lucky so far because he also isn't running mud flaps with 38's. Maybe if you cover the tube door with fabric they won't care.