Essentially, there is already a list of misdemeanors in California law which would make it illegal for a "convicted person" to possess a firearm for a period of 10 years.
This bill merely adds to that list (of penalized misdemeanors) the misdemeanor of "hate crimes", which are predefined as follows:
Existing law makes it a misdemeanor to, by force or threat of force, interfere with another person’s free exercise of any constitutional right or privilege because of the other person’s actual or perceived race, religion, national origin, disability, gender, or sexual orientation. Existing law also makes it a misdemeanor to knowingly deface, damage, or destroy the property of another person, for the purpose of intimidating or interfering with the exercise of any of those constitutional rights because of those specified characteristics.In order to save you the effort of searching the web (as I have just done) to find the referenced laws, I'm included a copy under the break.
You can see the entire section of law here.