I just got this item in one of my campaigns and put it on the Owlbear we tamed. Now the Owlbear is self-conscious and depressed and won't let us take it off.

Yeah

When I equip this on my D&D Beyond character, it raises every skill bonus by 4.  Shouldn't it only increase intelligence based skills?  Does this occur for anyone else?

Can you get the headband in the lost mine of phandelver? I really need it.

Sounds like a bug to report if raising non-int skills

Yeah I submitted a ticket yesterday. It seems to only happen when I equip a certain homebrew sword I have. No other homebrew items affect it. Super strange.

I have a character with 4 int and they are buying the item and it will be hilarious when he attunes to it. 

This is the item the brilliant ogre has in Baldur's Gate 3 Act 1 because he ate some poor creature wearing it. I love it.

no

This is insane, my Dragonborn had a 9 in intelligence before using this.