Imagine if everyone used technically jargon differently (Note: in many ways 'reductio ad absurdum' is technical jargon for logic).
We are on an RPG message board. If we were on a philosophy message board, this might be relevant, but we are not. Jargon has its place, but holding people to technical standards in non-technical settings it a terrible idea.
And while I agree words don't always need champions, there's times one certain word usages should be championed. There's only one simple way to refer to the logical argument of reductio ad absurdum and confounding that term with an outright inversion of it's meaning isn't helpful to anyone.
Pretending that this hasn't happened isn't helpful to anyone. The cat is out of the bag. This is how language works. You might think it's unfortunate that you now have to be more specific when describing that type of argument in certain settings, but that's how it is.
Moreover, using a term such as reductio ad absurdum in a non-technical setting such as this is a bad idea anyway. The fact that it's jargon mean you're going to have to explain it regardless, so using the term itself is not helpful. If you're going to engage in a reductio ad absurdum argument (in the technical sense) in this context, just do it. Don't label it. You're going to have to explain the label anyway, since this is not a philosophy board.
So ultimately we're not losing anything. In non-philosophical circles, you'd have to explain what you mean by the term anyway, so there's no additional work created there. And in philosophical circles, people will know the jargony usage of the term anyway, so there's little chance of confusion there.
It started as someones misconception over what reductio ad absurdum actually meant and was amplified via the internet.
How it started is irrelevant. How it's used now is the only thing that matters. A word's etymology is not its meaning.
This is different than a word expanding in meaning due to popular idiom and analogy. You mention the term crusade below and that's precisely how it's meaning was expanded. There's other words today that have undergone and are undergoing the same process and you don't hear me being prescriptive about them.
Indeed, and if you're not prescriptive about them as well then you're engaging in special pleading. Words change in meaning over time. Calling one new meaning "correct" and another "incorrect" is untenable, if the basis is that the meanings are different than the original meanings.
And yet today, people using red and blue in such a way would be doing so incorrectly. That's no different than using reductio ad absurdum incorrectly today.
It's very different. The proportion of people who use "red" to mean "blue" are vanishingly small. The proportion of people who use 'reductio ad absurdum' to mean 'appeal to extremes' is much, much higher. You pointed out how it started, and how it has propagated via the internet. So there are a large number of native speakers who use it with that meaning. That means it has that meaning. A word's meaning is determined by how people use it, so if a significant number of people use the word that way, the word has that meaning.
I don't think it's common, perhaps not rare either. But that usage began via misapplication and misunderstanding.
How a word came to be used in a particular way does is its etymology. Etymology does not determine current meaning.
Someone used the word reductio ad absurdum incorrectly and others unknowingly picked up on that incorrect meaning. It just so happens that now the meanings are polar opposites. One is a valid logical argument and the other an invalid logical argument. Surely even an avowed anti-perscriptionist as yourself sees the issue there?
Calling them polar opposites is dubious at best. The 'incorrect' meaning is "a fallacious use of the type of argument referred to in the 'correct' meaning." It refers to a subset of that type of argument. It is, in fact, a common linguistic phenomenon for a word to come to mean a specific subset of an earlier, more general meaning. The word 'meat', for example, used to mean 'food.' Now it means only a specific type of food. This happens all the time.