The uniform your grandfather is wearing is that of a Knight Templar, of which knightly a Trinitarian Christian Mason is invited to join. Of course, becoming a Templar is not a requirement and the Knights Templar organization is separate and distinct from Ancient Craft Freemasonry. According to the documents you forwarded to me, he was a member of the Santa Monica Knights Templar Commandery.
I have copied Sara Nelson in our membership department so she may assist in looking up what Craft lodge he attended; these are the only records the Grand Lodge of F. & A.M. of California keeps
Adam G. Kendall, P.M.
Henry Wilson Coil Library & Museum of Freemasonry
Grand Lodge of F. & A.M. of California
1111 California Street
San Francisco, CA 94108