A folder should in no way effect an objects rotation or orientation, however don’t quote me on that.
The most likely culprit is cloning the model from ReplicatedStorage to Workspace is messing with the welds and producing some funky results, have you considered keeping the model in Workspace and using Model:MoveTo or Model:SetPrimaryPartCFrame to move him into position as opposed to cloning him?
May I also chime in and say that your setting of the C0 and C1 of the welds seems slightly redundant considering it should be automatically set if the hair is in the right place.
Once again, I urge you to experiment with my suggestion that was evidently skipped over and would spare you the trouble of using script created welds in the first place. I also fail to notice why you create such a hassle of cloning just the hair into Workspace from ReplicatedStorage and not the entire model with it (also would save you a lot of trouble).
And to echo @Scottifly’s suggestion, if you turn the hair into an actual Accessory with the proper values, you can use Humanoid:AddAccessory to essenially automatically weld the item.
All are better solutions than pulling at straws with cloning the hair.