My first experiences of this word were in relation to moot court scenes in The Paper Chase (that [AmE] show/[BrE] programme was one of the early influences leading to my academic career). (Moot court is a trial practice exercise.) Then there was a sketch on Saturday Night Live that has stuck in my mind for 22 years now (I can't believe that I'm old enough to type that). In it, Jesse Jackson (the guest host, who was running for president at the time) was the host of a game show. He'd ask a contestant a question, and when s/he tried to answer it, he'd interrupt and say "The question is moot!" and then he'd embark on a diatribe about how it doesn't matter when Halley's Comet will appear (or whatever the question was about), because the Reagan administration is going to get us all killed in a nuclear war (etc.). You can see a video of it here.
As that example demonstrates, moot in North America is affected by its American legal sense:
An issue presenting no real controversy.You can see how this relates to the moot court experience--the exercise is academic and will have no real effect on the world. Meanwhile, in BrE, moot retains the sense 'debatable'. So, in BrE a moot point is one that can/should be debated, while in AmE it's one that isn't worth debating because the issue is already decided or out of our control.
Moot refers to a subject for academic argument. It is an abstract question that does not arise from existing facts or rights. --Thomson-Gale Legal Dictionary (US)
The American Heritage Dictionary gives some context for this meaning variation in the following Usage Note:
The adjective moot is originally a legal term going back to the mid-16th century. It derives from the noun moot, in its sense of a hypothetical case argued as an exercise by law students. Consequently, a moot question is one that is arguable or open to debate. But in the mid-19th century people also began to look at the hypothetical side of moot as its essential meaning, and they started to use the word to mean “of no significance or relevance.” Thus, a moot point, however debatable, is one that has no practical value. A number of critics have objected to this use, but 59 percent of the Usage Panel accepts it in the sentence The nominee himself chastised the White House for failing to do more to support him, but his concerns became moot when a number of Republicans announced that they, too, would oppose the nomination. When using moot one should be sure that the context makes clear which sense is meant.Whether there's anything that I can add to that is a moot point!