For some time I've been using Apachii SkyHair mod. Imagine my surprise when I wanted to change my pc's hair to something more Nord looking and I realised that the vanilla hair is clipping through my Dragonplate/Yngol Helmet. Anyone knows a mod that can fix this? Was this in Vanilla or I messed my game with mods?

I'm pretty sure that's a mod bug. If I understand how the engine works correctly, the game stops rendering hair completely when you're wearing any of the vanilla helmets like that (in essence everyone is bald under their helmet, which is why you don't see Argonians with horns sticking out the back and whatnot), so something is preventing that from happening. I haven't played with that helmet specifically, so I can't be positive, but I'm reasonably confident it's not vanilla.

I turned off both Open Face Helmets and Apachii... still the same.

did you try un-equipping and then re-equipping the helm?