One peculiar fact about USA presidents is that all of them from Woodrow Wilson on in have sported clean-shaved faces. The closest call the White House got in regards to a bearded president post-WW2 was GOP nominee Thomas Dewey in 1948, although he mostly had a short, unimpressive stache.
So, the challenge here is to, with a PoD after 1950, concoct a scenario in which a bearded man gets elected PotUS. Bonus points depending on how impressive his beard is and how recent the PoD.