That's a great question, and I think it's one still being answered at this point. Assuming that they are contagious (and there does seem to be some conflicting evidence here, which may mean it behaves differently in different people), it would work like any other person to person transmission. Your asymptomatic carrier would release respiratory droplets when talking (far more when talking loudly), coughing or sneezing (which could be due to allergies or just random coughs or sneeze we all experience from time to time), singing, or otherwise exhaling through their mouth. Another person breathes in those droplets or gets them on their hands or face, and the virus is able to find a new host.
Given the death toll already taken on the US and the relative risk of being an asymptomatic carrier, isn't it better to be safe than sorry? Particularly when in crowds indoors (e.g. grocery shopping) or visiting older or otherwise vulnerable (e.g. immunocompromised, cancer patients, HIV/AIDS, etc.) people? I know I don't want to be responsible for anyone getting an illness that ultimately kills them or permanently damages them if there's any reasonable way for me to avoid it.
My thoughts: Assuming I’m NOT sneezing or coughing - which is the vast majority of the time - then I’m also not singing or exhaling vigorously through my mouth as I walk thru a store, etc. It would be different if I went to a gym, but in a store? I breath thru my nose and rarely open my mouth. Any exhaust is directed downward thru my nostrils toward the ground and I will almost never be within 6 feet of another person regardless.
From the little data I’ve seen, I think the WHO got it right once when they said it was “very rare.” Then backtracked because that didn’t match the meme.
“...isn’t it better to be safe than sorry? Particularly when in crowds indoors (e.g. grocery shopping) or visiting older or otherwise vulnerable (e.g. immunocompromised, cancer patients, HIV/AIDS, etc.) people?”
If I needed to ride a subway, I’d wear a mask. If I needed to visit someone with a compromised immune system, I’d wear a mask. But those things just are not part of my lifestyle. Ever.
Meanwhile, it is often topping 100 degrees here in Arizona. Masks fog up my glasses (since my air is escaping ANYWAYS). They are the Prius of the ChinaVirus - virtue signalling without achieving anything for me. And I don’t believe in that.