Doing export business as foreign entity
Generally speaking, if you can stay away from California, you should. This is not the friendliest of states when it comes to taxation, and one of the smaller examples of the added burden a business takes on itself when registering in California is the notorious franchise tax of $800 (minimum) a year, among other things.
With that being said, if you are in fact in California and you are running the business from that state then not registering is not an option, and you need to form a foreign entity of the NY LLC in California. To learn about all potential tax implication I would strongly recommend you to consult an accountant in California.