First up, a characteristic example.

Often, the mustachioed fireman gets to drive the firetruck. Occasionally, he also gets to wield the axe with which to chop down your door.

See? Even in real life, the mustachioed fireman is an axe-wielder.
In this example, note the mustachioed fireman's joy at the dragon's inability to properly hold the hose.

Does he even want the house to be saved? Are mustachioed firemen agents of evil? Well, maybe not, because here's a Sesame Street example, and, with the possible exception of Elmo, Sesame Street is no place for agents of evil.

This is what I'm talking about, though. Sesame Street taught the world that two guys can live together in an apartment without corrupting anyone, that angry creatures live in the garbage, and that vibrating giggling monsters make good toys for 3-year-olds. Clearly they're open to outside-the-box thinking, and yet they bought into the mustachioed fireman trope.
One last literary example:

Okay, I might have doctored the last one. But still! They're everywhere. And in fact, lest you think the phenomenon is limited to literature, I bring you:
We had this guy sitting on our Fire Shelf at my last library in the Chicago area. His jacket is closed by velcro, and at said library, the velcro had been destroyed by years of use. Most evenings he could be found sprawled on the floor with his coat hanging open, looking like he just finished a bender. I will state for the record that this is the only evidence I've seen that mustachioed firemen drink too much.
So what should we conclude about the mustachioed fireman? Is it a coincidence? A conspiracy? Maybe it's just real life. I know only one actual firefighter, and he does, in fact, have a mustache. And given that he is my father-in-law, I won't say here that he is involved in any mustache conspiracy. On the other hand, I'm not going to say he's not.