Does council opinion matter?
Solution 1:
It generally has no effect - they all perform their jobs without any penalty.
However, they do count as being in your court, and so get a bonus to plot power against you (and disliking you, they are quite likely to join in plots against you). Furthermore, your spymaster gets a massive bonus to plot power against you as well. Definitely don't let someone who hates you become your spymaster.