In the cult I was raised in, beards were forbidden with the claim that it might give the impression of being revolutionaries. In the above, the argument seems to be of rebellion. On the other hand, it's all in the eye of the beholder.
Jesus was revolutionary enough for some ancient people to have written legends about him. Cults themselves are usually highly counterculture. The way we dressed in the cult I was raised in was based on old fashions and the youth who would try to stay in the classic style but were concerned with fashion might look strange.
For men some might look like a mobster or bodyguard, for women, like somebody attending a wedding or sometimes an old time farmer. In all cases, the members looked like out of place artifacts. I admit that I'm a modern city guy in Canada and that the cult comes from the US, so that may play a role.
But if the goal was to try to mix in and avoid attention, it was a total failure. :)
Also, if we think about it, shaved faces and neckties have a military origin, which would be a good enough reason for the apparently anti-war cult to avoid those practices, but no. It's not really rational, just the fashion statements of old men dictating how people should look in their outdated view.
And I'm saying that as someone who likes to look rather generic. I'm not an ads signpost so also don't wear stuff with prominently visible brand names or logos. But I don't care if you do, it's none of my business if it's not me.
A little parodic story:
A beautiful gipsy woman was shopping on a city street. Some angry white men started to bully her about her skin color, skirt and nose piercing. A particularly hateful white thug suggested to stone her. Jesus came about, noticing the noise. Verily, he said: "may the man who never sinned throw the first stone." The angry white men strangely felt powerless and they left her alone. But instead, they now attacked Jesus: "Who do you think you are? Woke libtard! Globalist! Marxist commie! Jew!"
Years later one of the angry white men died. He met Jesus again. As a good Baptist Republican bully who loves guns but not baby murder, who hoped to marry his sister who belongs to him and wants women to live fulfulling kitchen slave lives, who hates the people of other religions and who even rejects the evolution doctrine of Satan, he thought that he was saved. But Jesus told him: "I do not know you."