@Aladdin M.,
I can't speak to your rights in California... hopefully some else will chime in who can share this information.
On the appraisal front, things were very confusing and lenders were attempting creative workarounds to traditional walk-through appraisals. My company (Guaranteed Rate) was letting appraisers use Facetime or Skyp to see the interior of the property, for instance.
A few weeks after we instituted this practice, Fannie Mae and Freddie Mac came out with clear guidance:
If your landlord is doing a "cash back" refinance (taking more than $2k of cash back or paying off a second mortgage that wasn't used to buy the property), a traditional interior inspection will be required.
If they are not taking cash back, for the most part "desktop" appraisals and exterior-only appraisals can be used. Leniency is greater if both the old and new loans are owned by Fannie Mae or Freddie Mac (Fannie to Fannie or Freddie to Freddie). There are web sites where your landlord can look up who owns their loan. (Fannie here or Freddie here.)
I'm being careful to check the ownership of any loan i'm refinancing with no cash back and locking the loan with these rules in mind -- for everybody's safety and for simplicity.
There are lenders who sell only to Fannie or Freddie, which may stymie their ability take advantage of some of this flexibility (Wells Fargo is a Freddie shop, as is US Bank, B of A is a Fannie shop, pretty sure Chase is too.) Working with a lender with access to both Fannie and Freddie gives more flexibility. I've always chosen to work for companies with access to both (and lots other investors) which is nice when shopping for loan options for a client -- but now it can be a matter of health and safety!
A couple of other notes:
A lot of loans can be done with no appraisal at all -- waivers of appraisals are fairly common on purchase transactions and no cash back refinances when the property is owner-occupied or a second home. I don't see many (if any) on a cash-back refinance or when the subject property is a rental.
Loans that are above the conforming loan limit ("jumbo" loans), and other portfolio programs have different rules and may require an interior inspection. Th VA has offered leniency on their appraisals -- FHA has not. You're in California where the odds are higher that your landlord may be seeking a "jumbo" loan.
Back to your specific situation: You need to know more about your landlord's requested loan and lender than they may want to share to know if any options exist... but your landlord may not be aware of or have asked about alternatives.
If there's no way around an interior appraisal, I'd suggest asking to talk to the appraiser ahead of time and see what precautions they're taking. More than likely they'll be wearing PPE and will try to get in and out quickly (for their own safety and yours). If you open all doors, turn on all lights (and open windows for air circulation). The appraiser can move through quickly and take the minimal notes and photos they need without touching anything -- they can get measurements and do all of the rest of their work outside.
Good luck!!
Julee