In order to carry out this function, it will have to become, first of all, a peacemaker, interested in finding common ground among currently warring opinions. It will have to become much more radically pluralist than it currently is, hospitable to all publics, rather than identified with its preferred public.
This is literally the opposite of the lesson that all successful news outlets have learned in this century. The majority of people identifying themselves as centrists think they don't need news because their rationalist egos think themselves capable of being opinionated on everything from first principles. Rightwing media survives by catering to rightwing views. CBC will never earn the favour of the anti-government aisle. Its only sane choice is to try to lean towards objectivity but without really wasting time both-siding issues because clearly most modern issues have a straightforward right side of history to be on - this game of playing devil's advocate on shitty positions only alienates their real viewers.
The CBC's audience are people who believe a public broadcaster is a social good AND that social good deserves taxpayer funding. The Venn diagram of this group with modern politics is almost a perfect circle on top of progressives.
Regardless of CBC's attempts to cater to their mortal enemies, if/when they get to power, the axe is coming.