If you want a beard, you can join Special Forces. If not, then shave.We don't have a military full of Nordic pagans.
Not full of them, no, but it is a recognized religion in the service. The VA offers Thor's Hammer headstones, number 55 on this list, and to my knowledge at least two servicemembers are buried under them.
Naturally I support accommodation for genuine religious traditions in the service, which in the case of beards also means the Sikh. (They also have an approved headstone: number 36). In general the desire to restrict religious expression is baleful, and if it were to be invoked for any reason one might think of another religion -- sometimes but not always associated with beards -- that would be the most obvious candidate. It wouldn't be because of the beards.
The usual reason military (and fire) services discriminate against beards is because of an alleged difficulty getting a proper seal with protective breathing equipment. This is a misconception; I've used the stuff and it works fine. Hair is dead skin like skin, and with adequate pressure protective masks mate down just as well over hair as over flesh. Bearded men also uses equipment like CPAPs without difficulty.
Patel, meanwhile, looked rather foolish invoking what is usually a military phrase -- The Hill cites the Navy and Marine Corps, but I've also heard it used for the same Green Berets Hegseth is willing to grant beards -- as Kash is a Hindu-raised man who was praising a devout Protestant Evangelical Christian. Not, however, as foolish as the idiots who decided to treat "See you in Valhalla" as neo-Nazi code. Those people are desperately trying to wish into existence an opponent they would rather have instead of the ones that they do.