I believe CA has a preemption law that says no local city or county can enact laws more restrictive then CA state law. So in my opinion they don't have a leg to stand on.
That said when researching CA preemption law this is all I find.
53071. It is the intention of the Legislature to occupy the whole
field of regulation of the registration or licensing of commercially
manufactured firearms as encompassed by the provisions of the Penal
Code, and such provisions shall be exclusive of all local
regulations, relating to registration or licensing of commercially
manufactured firearms, by any political subdivision as defined in
Section 1721 of the Labor Code.
53071.5. By the enforcement of this section, the Legislature
occupies the whole field of regulation of the manufacture, sale, or
possession of imitation firearms, as defined in Section 12550 of the
Penal Code, and that section shall preempt and be exclusive of all
regulations relating to the manufacture, sale, or possession of
imitation firearms, including regulations governing the manufacture,
sale, or possession of BB devices and air rifles described in
subdivision (g) of Section 12001 of the Penal Code.
In the above I do not see CA stating no local municipalities may restrict carry of fire arms only registration.
What gives? Am I missing somthing? Please help me understand. Post the CODE that has to do with gun preemption laws.