You are on a military base, you are subject to military law.
While I do not know of any CA law explicitly prohibiting driving without doors, the doors on the TJs are subject to new Federal side-impact crash testing standards (which were put into effect in the mid-ish 1990's). So, TJ doors are in effect Federally mandated safety equipment. AFAIK, federally mandated safety equipment cannot be removed from any vehicle that is to be operated on public roads. So technically, it is against Federal law to remove the doors from a TJ and drive it on the street. By extension, even tube doors on a TJ or JK would technically be illegal for use on the street. I could be wrong, but this is how I've interpreted the law.
BTW, I'm not a lawyer, but I did stay at a Holiday Inn Express once.