In the past week San Diego county supervisors passed a “temporary” ban on evictions (except for ”imminent health and safety threat”) and set maximum rent increases at the CPI. 

No this would get worked out with the lender and the lender decides the cash flow is down or the original DSCR is in threat

WOW This tenant just left a 3min voice mail yelling at me why I am by their place and I am threating them by being around their home.

Cyber Liability. 

My question is it legal for me to deny an applicant in this situation because of the disruption to other tenants, threats to their health and safety and additional costs? 

BUT, would you be able to sleep at night knowing that one morning you might get that cease and desist letter with some horrible legal threat coming from the city?

Basically, if they have a doctor's note stating that they require said animal due to a disability, you can't tell them no, unless:- There is reliable objective evidence that the animal poses a direct threat to the health or safety of others that cannot be reduced or eliminated by a reasonable accommodation;- There is reliable objective evidence that the animal would cause substantial physical damage to the property of others;- The presence of the assistance animal would pose an undue financial and administrative burden to the provider; or- The presence of the assistance animal would fundamentally alter the nature of the provider's services.Unfortunately, deposits or pet surcharges are not allowed for animals covered by these laws.Now, all this said, landlords in my area usually just deny or evict folks with doctor's noted pets anyway and I've never seen someone bring suit.

The rent control veto threat was probably easy.

Probably 80% of the listings we deal with are homestead, and I think not only would that be refernced in the right of specific performance section in the FARBAR, I would have been made aware in the couple of specific performance threats I've been involved in.

Sounds like you are dealing with a "child" who is making threats to get their way.