Legal Question in Employment Law in California

They are not only allowed to, it makes very good sense, to avoid any claims of misappropriation of company property. This would seem to be for your protection as well as theirs. Why would you not want your tool box to be photographed? They are just tools.

They are 'allowed' to do anything thing they like, subject only to criminal or illegal discriminatory conduct. This isn't it. The employer is entitled to set and change hours, duties, titles, compensation, benefits, leaves, vacations, holidays, policies, rules, etc. You have essentially no 'right to privacy' on the job except in limited circumstances, such as bathrooms and changing areas. Mr. Kirschbaum is entirely correct; this is an intelligent business policy that could be usefully copied by similar businesses. It appears to be designed to document your property so as to protect them from employee theft of their property, and you from theft by others.