The 19th century could be considered the golden age of facial grooming. Looking at the 20th century, we see a continued interest in mustaches during the first decades, but gradually, mustaches fall out of favour. In the latter half of the century, the beardless mustache is more and more associated with subcultures or "others", non-Europeans. Why did it happen? I can speculate on several reasons. The mustache has always been a symbol of privilege. In many European armies of the 18th century, only officers were allowed to wear a mustache. With the democratization of Western culture, the mustache acquired a taint of aristocracy and backwardness (one might ask why the moderniser Kemal Atatürk, for example, shaved off his mustache). On the other hand, mustache-wearing has been seen as obligatory for men in many Southern European countries - as well as Arab, Turkish, and South Asian cultures. For example, in Italian regional proverbs, the mustache is a symbol of sexual prowess, and it is not surprising that the celibate priests were not expected to sport them (full beards are a different story - with a full beard, you're a patriarch, a revolutionary, a mystic, larger than life!). Perhaps the decline of the mustache was a new phase in the development of the Western bourgeois masculine ideal, as it became a trait of villains, often foreigners.
One thing is sure: The mustache had a rocky career in the dream world of Hollywood, often opposite to its popularity in the "real" world. Behold mild-eyed, Scottish-born Welshman David Powell (below, with Billie Burke).
"- Well, a mustachioed gentleman never looks quite correct, according to many. 'That's no good,' I once heard a couple of ladies utter when my likeness appeared on the screen. My acting was obviously of less importance. Due to the mustache, I was impossible from the very beginning. - On another occasion, I heard an older gentleman make the assumption that I surely was the villain of the drama - 'look at the whiskers'. The comment was incorrect, since my act at that occasion did not include any rascality or roguishness. - However, in a few of my latest films, The Firing Line and The Teeth of the Tiger - the latter currently in production - I believe that my mustache will be in harmony with the characters that I will play. In the first, I have to fall nobly in action; it is the prerequisite for the happiness of the heroine, Irene Castle, with Vernon Steele. And in the latter one I am very cruel; according to the script, I have to look like I had seven human lives on my conscience."- David Powell, Filmen 1920 No5 (my translation)
NB: In both of the films that Mr Powell mentions, he played characters with French names - in the latter, the great Arsène Lupin himself!