Centaurs and Satyrs are, like I said in an earlier post, an unusual case. It comes down to what they are in the setting. If they’re spirits of nature? Then it’s fine for them to have an essential nature. Are they people with societies and cultures and such? Then it isn’t. Personally, I lean more towards the “they’re people, and should therefore not be essentialized” interpretation, but there’s definitely gray area there.
There’s no such gray area with redcaps. They aren’t people, they are literal murder spirits. Is it possible that some day they will come to be viewed as people, or that the standard will shift such that even defining otherworldly spirits in essential terms isn’t considered acceptable? Sure. And if that day ever comes, they’ll probably be changed. But for now, I don’t think there’s a problem.