No. Wearing a beard is a personal choice made by people who practice Ásatrú, Forn Sidr, Norse Paganism and other forms of Heathenry, but it’s not required in Heathen practice.
The reason for this is because Heathenry is a decentralized religion without any doctrines or dogmas. There’s no ultimate authority (be it a book or a person) that determines what Heathen practitioners should do, including whether they must wear beards. Religions that mandate certain dress styles do so because it’s part of their religious doctrine.
Many Heathens choose to wear beards as tribute to Old Norse cultural values of good hygiene and healthy grooming habits. Long hair may also be worn in conjunction with the beard, especially since Heathen identity can also overlap with various musical subcultures where long hair is typical for all genders.
Any individual, group, or resource that claims beards are mandatory in Heathenry are enforcing their personal opinion rather than anything cultural, religious, or even historical.
The benefit of a doctrine-free religion means the choice of practice belongs to the individual, rather than a system. Because of this, Heathens can shave for settings where high sanitization is necessary, like in the military and in medical fields, without it impacting their practices.