Do you have any idea why sporting the moustache was so much more common in the military than in any other job in 19th-century Western countries, and to some extent present-day Western countries?

In Britain, at least, 19th-century military men were required by standing order to maintain a moustache. The order was not lifted until 1916.

This UK Telegraph article discusses it.

For more mustache information, feel free to consult
Mustaches of the Nineteenth Century. The one-stop blog spot for your Nineteenth Century Mustache needs.