I don't play my inquisitor to mirror my own personality, so I get disapproves of people who I as the player agree with...
I get disapproves from Cassandra all the time because I say I'm not the chosen one (don't believe in the maker), and because I play a bit cheeky/defiant, but mostly polite. But she's my favorite character and I admire her resolution.
Personally I agree with Vivienne quite a bit surprisingly, but my character wants the mages to be free, so she hates me...
Companions whose personality and world view *I* approve of and identify with the most:
Solas
Cassandra
maybe Dorian
Somewhat approve:
Vivienne (opinion on mages NOT her condescending attitude)
Blackwall
Varric
I have issues with:
Sera
Iron Bull
In-game
Approve
Solas
Dorian
Varric
Mixed reactions
Cassandra
Iron Bull
Blackwall
Dissapprove
Vivienne
Sera
Only just got Cole...