Is
it permissible for the Muslim to deal with ribaa in a society that is
based on ribaa?

Praise be to Allaah. 

It
is not permissible for him to deal with ribaa, even if the society is
based on ribaa, because of the general applicability of the texts which
forbid ribaa. He has to change this evil action as much as he can, if he
cannot move away from that society in order to distance himself from this
evil, lest the punishment that befalls them befalls him too.

 And
Allaah is the Source of strength. May Allaah bless our Prophet Muhammad
and his family and companions, and grant them peace.