I also reside in SoCal OP, San Diego to be specific and think as long as the rain is light and the air is not too cold and windy, then walking would be okay.
However on the day you mentioned, it was very windy and rainy for the majority of the morning so my bosses didn't expect me to walk anywhere. If they did, I wouldn't have been too happy.
Even though the weather was warm and muggy, I still would have extra work to do. Changing my charge's clothes and diaper immediately upon arrival, drying off the stroller as well as mopping up any extra water on the floors and putting out charges shoes to dry while drying the wet clothes in the dryer. Not to mention if I do not have an extra clean set of clothes, drying my own stuff.
And even if I did have an extra set of clothing, I would have to find a place to store my wet clothing too.