There are limitations but it's not a full ban.

How many communities ban rentals?

Just look at the myriad of laws, regulations, and bans passed or proposed for seller financing, wholesaling, and lending in the past two years.

But then they also banned foreigners from buying in the major cities.

All my agents are BANNED from doing ANY showing of any kind to ANYONE even a family member, their priest, their wife, I don't care who it is or why NOBODY get's a showing without signing SOMETHING. 

The HOA is money hungry so they will never ban short term rentals. 

My mgt s-corp is also who HUD Section 8 or CAC or other entities pay and 1099. 

Quote from @Conrad Legé: I did a search and don't see a ban on searching criminal history.

CA is not STR friendly as evidenced by SB584 and the various communities that have banned/limited STRs. 

Think, the USDA brining armed feds to shut down Amish farmers for selling their unpasteurized milk, or the FDA allowing harmful chemical additives in our food that are banned in hundreds of other countries.