This is essentially what had to be dismantled in Northern Ireland - it was under the control of one "group" usually defined as Protestant. Transferring it to a situation under human rights law where all religions could live with equal protection under the law (including protection from the state and police by means of human rights law) was critical to ending the conflict.
None of the Catalan, Basque (this is the usual English spelling, are you perhaps thinking of the Russian Басков?) or Scottish independence movements have ethnic cleansing ambitions, although these are usually attributed to them by their enemies.
Construction and definition of a nation state is a complex issue not reducible to glib remarks about "liberty".