A panel of California lawmakers voted to exempt large categories of information, the insurance industry, and automobile manufacturers from the state’s Consumer Privacy Act during the landmark law’s first legislative committee review.

The Assembly’s Privacy and Consumer Protection Committee approved nine bills with bipartisan support April 23. Among them are measures to narrow the definition of personal information and explicitly allow information sharing for customer loyalty programs, in addition to those exempting some information and industries from the law’s disclosure and privacy requirements.

Business and consumer advocates are pressing lawmakers to carry through on their commitment to fix the law...