(from the title) thought zillow was taking these vaccine mandates very seriously... 

Plus, the vaccine is getting rolled out which will curb the spread tremendously.

No one will ever care about vetting that tenant as much as you and its a great learning experience.  2) Keys should never be handed over until you have copies of all utility transfers and verified, renters insurance, rent for the 1st period due, pet insurance/vaccinations or any other its required in your lease. 

However, since the vaccine rollout started, I saw more and more people moving back to the bay, and I'm confident most tech companies in the bay area are going to adopt a hybrid working model instead of a 100% remote model, which still requires people to live close to the offices/campuses.3.

Proper Vaccination during Rental period2.

Plus, the vaccine is getting rolled out which will curb the spread tremendously.

I am not sure if it is state by state, but I know in Connecticut you can NOT charge any increase in rent or deposit for ESA or SA.One thing I do is request to see the documentation that the animal is properly vaccinated & licensed, I also ask for documentation of the animals training which I have 3 tenants with approved SA's and of the 3 none had any issue showing the information requested. 

I have the rough goal start looking for property in earnest after my second dose of vaccine in April.

I think it was here before March 2020, and I suspect even if a vaccine is developed and widely available in the next 6 months, not everyone will be vaccinated (yet).

Then depending on a lot of things like vaccine, elections, economy, rents will start to slowly improve in 2022.