You're conflating two different things, so let's separate them please.
1)
Network TV is supposed to be neutral. Cable can do whatever they want.
CNN & FOX are both the exact same 'cable network TV' and if one is 'supposed to be neutral', so is the other. There is zero distinction between them, I don't know why you keep on implying there is.
2)
Fox and MSNbc chose sides, and it is stated by their founders. CNN purports to be neutral
What you seem to be saying here is that Fox is honestly partisan whereas CNN is falsely masquerading as neutral. I have no argument with that, I'm happy to admit CNN is perhaps morally inferior to Fox and is more misleading.
My point is Fox playing more of a role in shaping Republican voters behavior by provoking an emotional anger at the other side and identifying us vs them. This is done by saying
all democrats are bad. I could be wrong, but I don't believe CNN plays that much of a role in shaping democrat voter behavior; they never try to portray
all Republicans as bad. The fact that they're reporting biased news isn't making voters vote one way or another, anybody watching CNN knows they are getting a more liberal view and anybody who wants to see the right wing perspective simply changes to Fox.