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