It's a dog whistle. Everyone who's been in the army with an ethnically mixed population knows many black people (think West African mostly) have severe skin issues if they shave fully. I had two guys in my section (so I assume more in the company but I can't recall) with exemptions and, of course, they were black.

The military started banning beards in WWI because they don’t work with gas masks (RIP cool civil war beards). They were only allowed again during the global war on terror because American soldiers were basically jealous of Afghani fighters’ full beards. Type of shit that’s too goofy to make up

I'm pretty sure "beardos" is only there to rhyme with "weirdos".