To "be held accountable" or to "hold someone accountable" is to measure up to a certain standard of living or doing things.

It sounds like this context is difficult, but some examples of holding each other accountable are:

"When I run with my friends, we hold each other accountable to the distance we are running."

"When my family wants to be healthy, we hold each other accountable to what we eat"

The sentence could be re written like this: "I think that only by making sure we all do our part given the privileged identities we carry, can we move forward into a society where those identities no longer predict life outcomes for the marginalized.

I think it means that by "watching each other and make us responsibles and concious, you for me, and I for you, of the benefits we have in the society, then we can move into a society wjere those benefits are not the only thing that predicts outcomes for the marginalized." Hehe I hope I didnt make it.more complicated :P