i think my only solution is to use another hairstyle collection:
https://steamcommunity.com/sharedfiles/filedetails/?id=1787545902&searchtext=splatoon+hairstyle+colours+and+parts like this one

I have that item installed but I'm still getting checkered textures.

Originally posted by mdestroyer27:

Help me, almost all of the hairstyles have a checkerboard reflection on them and I don't know how to get rid of it. I have tried reinstalling the addon and reinstalling gmod but nothing works. Plase help me with this problem, thanks

I'm having this issue as well. But it's very unlikely that the guy who posted this mod to the workshop is ever gonna see this and get around to fixing the mod. It hasn't been touched for almost 5 years and it's just broken. I've tried all I could do, such as reinstalling TF2 (might try reinstalling GMod), verifying the game files, subbing to other Splatoon mods, etc. So far, nothing. So maybe the guy doesn't care about the mod anymore, or he's just busy or something. But this mod does need to be fixed for sure.

Okay. I have an update and solution for this issue. Good thing is that the mod isn't broken. But the model paths are very different and don't match, which explains why the textures show up as the weird checkered reflections on the models. And since this mod hasn't been touched in almost 5 years, it's sort of unlikely the guy who posted this mod to the workshop will ever get around to fixing the model and texture paths, but who knows? Anyway, the solution I came up with that works really well is to copy the original textures from the Splatoon 2 Cosmetics Pack (the required mod this one needs to work) using the Sub Material Tool, and then paste them onto the hair models from this mod. It won't work if the hair is already bonemerged onto the Inklings, so it's best to do this with just the hair piece models BEFORE bonemerging them onto the Inklings. Hope this helps.