The meaning of "mugwump"...

[robkelk]

... is, apparently, different in the UK than it is in the USA.

Cambridge Dictionary definition of mugwump:

US informal (also Mugwump)

a person who likes to be politically independent and does not support or remain loyal to any political group:
As a reporter, I've met with political groups large and small, Democratic and Republican, Green Party, mugwumps, you name it.

UK informal old-fashioned

a stupid person:
To make a fresh milk cheese at home is the simplest of processes; any mugwump can do it.

So, is "Supreme Mugwump" Dumbledore a person who by definition does not take part in partisan politics, or is he the biggest idiot?

[Bob Schroeck]

As I recall, the Mugwumps were a political party in the United States during the early-middle 19th century. Humorist Richard Armour, in his book It All Started with Columbus, described them as dedicated fence-sitters, "with their mugs on one side and their wumps on the other" (a phrase which has stayed with me for more than 50 years, along with my memory of the associated illustration).

I suspect that's the sense in which it was intended. But given what we know of the Wizarding World... <grin>

[classicdrogn]

Wekk, he's definitely not a political independent, thst's for sure. A bit hard to be, when you're the figurehead and usually direct leader for one of the main factions. "Stupid" only in the YA gwnre "all adults are useless" way maybe, but taken as a whole he's more like a minor antagonist (after Snape, Draco, Umbrage, and the Dursleys, but still beating Voldemort out of the top five for directness of action) from a story function position.