As a general rule, no officer can make an inspection into your automobile or residence without a warrant that requires probable cause. If exigent circumstances exist, then a warrant is not required but probable cause must be present. I am not licensed to practice in California (thankfully) so the state's supreme court may have decisions that muddy these waters, and perhaps the federal district courts have weighed in on this as well. I doubt they have changed the probable cause requirement, however.
The biggest issue against the State of California requiring anyone from submitting to any search or denying entry is that (1.) the U.S. Constitution allows for free travel without restriction, and (2.) except for just a few of the entry points into the state none are not subject to any inspection.