The specific reason at the time was the prevention of members of the "Mongolian race", meaning people of Japanese or Chinese heritage for the most part, from "invading" the area. Racial covenants might still be in the legal paperwork associated with some of these houses (but not the former house of a famous Senator - she famously took steps to get rid of the language). Regardless, any such covenant is no longer legally enforceable.
The good people at Google apparently didn't realize Presidio Terrace is a private street so they just drove in one day and snapped away. Take a tour! Just click on "Street View" and pick up the yellow man (yes, the Yellow Man!) with your mouse and show him through the gate indicated by the green arrow. Then click on "Full Screen" and use the little white navigational arrows to move about and the smaller black arrows to sit and spin. Enjoy.
[Kids, this "restricted residence district" started about 100 years ago, yes, but the covenants have affected the makeup of the hood more recently, and arguably, the legacy persists. The first non-white family moved in when, exactly? Mmmm.]