Strawmanning someone's position is about a rhetorical game. Fairly representing someone's position and pointing out that it is logically contradictory is exactly about truth. Self-contradictory positions cannot be right. (Now, you may be able to remove the contradiction without destroying the whole position. But it has to be flawed.)

You see this in formal philosophy. If the conclusions of an argument disprove the premise, then the premise is wrong.

In this case, we aren't dealing with a formal position. We aren't even dealing with the clearest-spoken advocates of a position. We're dealing with culture warriors whose specialty is yelling, not clear argument. Nevertheless, there are people out there who say that, if you say one culture is better than another, then you are a Nazi. This is not taking their argument to a logical extreme. This is listening to their words. And based on that, you can say that that position shows that they aren't thinking, because it's absurd.

But you're right, you can't go too far with it. The worst, most thoughtless advocates of a position only let you say that those advocates' position is flawed. They don't tell you anything about the steelman version of the position.