It’s my understanding — which seems to be congruent with the pages you linked? — that facial hair is an impediment to medical-grade respirators that require a tight seal to be effective. With cloth/paper masks that aren’t intended to be PPE for medical workers, though, that’s not actually what we’re going for, though, right? What we’re trying to do is curtail the spread of droplets. Beards and mustaches really won’t materially affect the effectiveness in that case.

In your specific example of volunteer health assessments and triage at a homeless shelter, you probably need real honest-to-goodness PPE, and the organization’s advice was wrong. When I’m going down to the grocery store, though, a cloth mask should be sufficient — and my (admittedly short) beard is not going to keep my mask from blocking droplets from my mouth and nose, assuming it completely covers both of them.

It's an impediment with any mask which can form some kind of seal. A surgical mask will stick to your face when you breathe in, which indicates that it does form an imperfect seal.

If one's beard is creating even more space between the face and mask, it's of course going to make things worse.

Cloth masks aren't trying to form a seal. They have a few roles:

1) They capture a lot of droplets coming out of your mouth. Do you sneeze in your elbow or in someone's face? A face mask does better than an elbow, and for every breath (not just a sneeze). So does a beard for that matter; if your sneeze goes around through a beard, it's catching big droplets too.

2) You know the six-foot-guideline? They effectively increase that distance. A person talking, yelling, sneezing, etc. can carry droplets 15+ feet in a straight line. If we're both wearing masks (or face shields), it's not going in a straight line. Beards disrupt linear airflow too.

3) You can't touch your face.

They don't stop virus aerosol. That's where you need a proper seal.

I'm not actually sure facial hair makes any difference with a cloth mask. Surgical mask would be in between. And an N95 probably becomes a surgical.

What would someone find offensive about the picture?

I guess the toothbrush mustache is verboten.

Possibly the labels under each facial style.

Offensive or hilarious? I love the creativity behind naming each individual style. I don't think any of them are particularly offensive, are they? It's possible I'm missing some references, of course.

Some people have a hitler mustache phobia.