I wasn’t around then, but I’m pretty steeped in 20th century popular culture. It seems to me, the 50s Beat culture began the whole “let your hair grow” thing in opposition to the very clean-cut trends of the recent past, and the Hippies in the 60s took that and ran with it. But it didn’t leave the counterculture and become something average Joes embraced until late in the decade and into the early 70s.
But a lot of hippies took it pretty far, not shaving at all, not their legs, armpits, or, for dudes, their faces. But as it trickled into the mainstream, it got more toned down. Women kept shaving their body hair, and rebelled through clothing, by not wearing bras, or wearing miniskirts and or blue jeans. Men’s hairstyles got longer, but they still went to the barber to keep them trimmed and stylish. And while shaving expectations were relaxed, men rarely grew a full beard. It was long sideburns, or handlebar mustaches, or goatees.
And in the 80s, as the “clean cut” look began to come back, the mustache seemed to be the last holdout, with Tom Selleck and a handful of other stars keeping them throughout the decade.
As to “why”, facial hair on men was almost exclusively reviled throughout the entire century up to that point. Only very old men wore beards between 1900 and 1950, and even among old men it was quite rare. In 1940, if someone said “Man, you need a shave”, it was probably like telling someone “you need deodorant” today. I suspect seeing those first beatniks with facial hair was quite a shock. Long hair on men, even more so.
For people of a younger age, I suspect it was just as shocking as spiked mohawks and leather jackets with a million zippers. Or “goth” makeup, dyed hair, and all black JNCOs with an “Orgy” t-shirt for an even younger demographic. Teenagers always love to shock their parents. By the 80s though, dudes with long hair and mustaches were the parents. So “clean cut” came back in order to differentiate.
And I’m already seeing more “clean cut” stars and a lot fewer hipster beards today than there were five years ago. These things come in cycles. In fact, the uniform lack of beards in the first half of the 20th century is far more interesting to me than the cyclical nature of facial hair since the 60s.
Yes, mustaches will become popular again, though I won’t hazard a guess as to when. Our society is very disjointed at the moment, so these fads tend to cycle at different rates now depending on the subculture, rather than in unison through the “mainstream” which I’m not even sure exists anymore.