Ask a this to a hinata fan.
Are you a Hinata fan? I bet they would like it in the end if it became truth. Mainly because Naruto would have to stop Sasuke from destroying her and it would be all lovey dovey with Naruto hugging Kaguya away because ya know...all she needed was some true love in her life and then she'd be at peace! :yayy:
That's exactly why this wont happen tho! Lol If it did, it would add an unnecessary element to the awesome amazing fight we are gonna see! So in answer to the OP, Naruto would react by flipping out and trying to find a way to save Hinata while keeping Sasuke from destryoing her. He'd sacrifice his life in order to save her even since she basically did the same for him with Pain. It'd be alright but like a 2/10 probably. Altho I do think there is around a 70% chance Naruto will sacrifice his life in order to save the world. Kinda why I think the SO6P's bro is not mentioned in all the legends.