I'm really curious as to if there's a reason that this century-and-a-half-old organization dedicated to racism and hatred dresses like schoolchildren told to sit in the corner for being stupid.
I've written on the topic of the Klan uniform before here. It doesn't focus too specifically on the pointed caps, but I would reemphasize what Parsons speaks of regarding the original Klan and costuming, which was heavily influenced by carnival style dress. To build off of what is in the linked post, as Parsons goes on to note:
The Ku-Klux’s costume and theatrical behavior resounded in many registers. To be sure, each of these costumes and identities had its individual valence. Moon-men evoked the idea of lunacy, dead soldiers the ravages of the recent war, Indians savagery, animals brutality. Yet all of them told observers that their wearers had adopted the role of the unfamiliar, unpredictable, and uncontrollable.
The point here being that they actually wanted to look absurd, and it was quite intentional.