I can't speak for California, but in my neck of the woods the membership would have to vote to decertify the current union, then vote again to join the other union.
A major obstacle to all that is that most unions have no-raid agreements with each other. So the new union would make it very clear, from the beginning, that it would not accept those members.
A second obstacle is that union elections are usually corrupt. Any decertification election would be rigged to fail from the get-go.
My thinking was why don't a group of teachers get together and form a tea party union. I doubt it could happen but it might be fun to try.