Well, if you ask some of my more hardcore conservative relatives, they'll say the CBC is so slanted to the left that it should have all of its funding revoked.
Personally, I've voted Conservative, Liberal, and NDP in various elections at various times. Every election, I print out each party's platform, make notes, watch the debates, and only then make a decision.
Approaching the CBC from that perspective, I've found them to be quite fair overall. They actually seem a bit hostile to whoever is currently governing. I've seen the hosts of some of CBC's political shows give government ministers and MPs from all parties a hard time, asking them tough questions and pointing out when they contradicted themselves.
I think you concern is valid, but I haven't observed it happening even though CBC already receives lots of government funding.