Sera won't be trusting the Inquisitor easily--that much I'm certain of.
I suspect that, in a way, we'll need to work towards gaining some characters' trust. How that works is anyone's guess at this point. I think Sera might be a little bit high maintenance, though. But once you have won her heart, there's no getting rid of her.
I don't think any, or very few, of the characters will trust the Inquisitor easily. Almost all of them have betrayal or disillusionment of some kind in their past.
Cassandra: The plot of Dawn of the Seeker details it. Then the situation in Kirkwall.
Blackwall: Something made him leave the Wardens.
Dorian: He's sick of the way his countrymen behave.
Iron Bull: Torn between two lives.
Leliana: Marjolaine and the situation in Kirkwall.
Cullen: The demon invasion in Origins, Meredith's madness and the mage-templar war.
Varric: He saw his hometown go to hell.
Cole: Well, he's all kinds of special, that one.
Solas, Vivienne, Josephine and Sera are the only ones I see as not having experienced that, but then we know little about them at this point.