Here's an example:
My first character, my dwarf, had a lot of trouble getting along with Sera. In most conversations, she was at least slightly disapproving of at least one thing my PC said, and much more in conversations after the Well. However, thanks to War Table missions and judgments, Sera got high enough affection with my character to do the Rooftop scene. So that's another trick I learned. Cass is much the same way; she likes the judgments where you give back to the people, such as sentencing the mayor to repay the village, or making the Dutchess do farm labor.
Same here. She was very irritated with me about all things related to magic and Mages and Elves (weird how often that seems to come up even as a Trevelyan), and I was have a really hard time not just save scumming and metagaming my way into her good graces (I promised myself I wouldn't do that).
It wasn't until that mission with the noble that she can potentially beat to death that things started looking up. I've never been so happy I took a perk before.
Cass was actually much easier for me than Sera, because there are plenty of opportunities to assure her early on that you have faith in her and respect her, while Sera doesn't open up to the player until later in the story.
It turned out to be pretty easy to reach full approval organically with most of them, even if you agree with them on just about nothing, provided you are actually trying to be their friend and help them with their requests.