"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.

Compare:

*The two went back London. (bad grammar)

The two went back to London.

It's the same comparison with your two sentences:

*go back being friends (also bad grammar)

go back to being friends

"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.

Compare:

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)

"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.

Compare:

*The two went back London.

The two went back to London.

It's the same comparison with your two sentences:

*go back being friends

go back to being friends

"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.

Compare:

*The two went back London. (bad grammar)

The two went back to London.

It's the same comparison with your two sentences:

*go back being friends (also bad grammar)

go back to being friends