It depends on the state constitution. For example, the Illinois State Constitution reads:
SECTION 22. RIGHT TO ARMS
Subject only to the police power, the right of the individual citizen to keep and bear arms shall not be infringed.
For comparison, the Indiana State Constitution reads:
Section 32. Arms--Right to bear
Section 32. The people shall have a right to bear arms, for the defense of themselves and the State.
The California State Constitution (and five other states' constitutions) say nothing about the RKBA. The state legislature can pass any restrictive law they think they can get away with. They are still elected officials, so I doubt they'll do anything crazy. But they could.