Google Ngrams says that go back to being friends is a lot more common than go back being friends.
Is the reason grammatical? Or there's another reason? (Or maybe they are equally correct?)
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"Go back" means "return", and "being friends" is a state. After having a falling out, two people may return to this state. Grammatically, this is the same as how they might return to their home towns after a road trip.
The two went back to London.
*The two went back London. (bad grammar)
It's the same comparison with your two sentences:
go back to being friends
*go back being friends (also bad grammar)