San Francisco is in lockstep with California's statewide reopening plan.
The city is not imposing any further restrictions regarding real estate activities, and, in particular, property showings and open houses. Click here to read San Francisco's latest health order of June 11, 2021. Also, see below for a summary of the statewide real estate opening plan as outlined by the California Association of REALTORS®.

CAR - SUMMARY & GUIDELINES: 
The California economy is reopening today -- Tuesday, June 15, 2021 -- and, with, limited exceptions, it is returning to normal operations

Are there any restrictions on open houses or showings?
The only legal restriction is for wearing masks, otherwise there are no restrictions. 
- No physical distancing is required. 
- No cleaning. 
- No posted rules of entry.
- No PEADs or any other type of sign in. 
- No one has to agree to an office prevention plan. 
- No one has to attest to their current health status.

What is the rule be for wearing masks?
Follow CDPH Guidance for Face Coverings (last updated on May 3, 2021)
According to this guidance -- unless everyone is fully vaccinated -- people must still wear masks indoors. 
As a practical matter, this means that:
Masks need not be worn during a showing if everyone is fully vaccinated.
But during an open house masks are required because even if a single unvaccinated person enters an open house, then everyone must be masked.

Who made this announcement and when?
The State of California's Department of Public Health issued an updated order on June 11, 2021. Click here to read it.

What about the color-coded county tiers? What if my county is in red or purple?
As of today, the system of color-coded county tiers is no longer in effect.

What about cities and counties? Can they continue to enforce more stringent local rules?
If a locality continues to enforce more restrictive rules, then it will be prudent to follow them.

My seller wants to require that everyone entering the property wear a mask or be vaccinated. Can the seller require this?
Yes. The seller can set their own rules as to who will be admitted to the property. 
The seller may require that everyone wear a mask. The seller may even demand that all people entering be vaccinated or show a negative COVID test.
Obtain the seller's instructions in writing. Your office may require that the listing agreement be formally amended (modified) to reflect these Seller instructions.

If the Listing Agreement Coronavirus Addendum or Amendment (C.A.R. Form RLA-CAA) has already been signed, the listing agent may want to now add a Modification of Terms. 
Write the following into the “Other” paragraph: “The RLA-CAA, dated ________, is terminated.”
For those sellers who want to keep certain restrictions on showings, you may want to add optional language such as, “with the exception of ______________________________________ .” or “The following showing requirements shall be followed: ______________________________________.”

For further information see:
CAR's June 15 Reopening Quick Guide
CAR's June 15 Reopening Q&A