We called a number of realtors in the Los Angeles/Beverly Hills/Malibu areas ... you'd think fears in L.A. would roughly match those in most of the country.

The obvious concern ... people moseying through houses have no idea about the medical condition of those in the house, the other lookie-loos and the realtor. And the owner has no idea what strangers are touching surfaces -- doorknobs, faucets, kitchen counters, etc -- that could lead to a very bad outcome.

The other side of the coin -- interest rates just went down again and it's super-cheap these days to get a mortgage, which is good for both buyers and sellers.

One big real estate company -- WEA -- is shutting down all of its open houses and even putting tight restrictions on showings. It sent a memo to its agents which says in part, "For the health and safety of all involved -- you the agent, strangers touring your sellers' homes and buyers interacting with other buyers -- they should be postponed." The memo recommends that all showings be with only one buyer (or family) at a time. But, the WEA official advises NO OPEN HOUSES for the time being.

Another major realtor tells TMZ, he's doing an open house tomorrow, adding, "Everyone is being cautious, but not coming to a stop. Hand sanitizers, Clorox, no shaking hands, but not halting work."

A big realtor from Coldwell Banker tells us, "We haven't seen a drop off in the number of people who are coming to open houses. People are still out there looking, especially with lower interest rates ... however, we are not shaking hands, we put out hand sanitizer for everyone to use and a sign stating that if you have a fever, cough or any symptoms of being ill, please do not come inside."

Another realtor is showing a celebrity home tomorrow but didn't want us to say whose, because there's such panic, it might affect the sale.