Pissing them off=huge hassle. She is going to consider whether gaining Ferelden through nonviolent means (save any rebellions) is worth it. And would the Chantry, if they really have a problem with Cailan getting a divorce, focus all their ire on him and be perfectly fine with the woman who marries him after he illegally (in their eyes) ends his marriage? Sure she can rule fine after pissing them off but the reason everyone doesn't just blow off their religious powerhouse is because it causes problems and if the payoff is not worth the hassle then they aren't going to incur needless hassle.
"Laughs" Sorry Sarah, but again I must repeat myself: You are defensive, seeking to please everyone out. Only a fool does that in politics and hopes to win. Celene didn't become Empress by being nice, but through assassination.
What will the Chantry do? Declare an Exalted March her? Celene is quite secure in her powerhouse in Orlais, and the Templars would be slaughtered like pigs. Excommunicate Celene? Well then the Chantry losses Orlais as it's base. ( and it might as well declare itself dead if that happens )
You are under the assumption that if Cailan rennounced Anora then Chantry wouldn't abide by it, but here's a shocker for you: There would be repercussions for the Chantry if they did that, since Celene has far more power then they do.
Secondly. The Chantry is more like the Orthodox Church under Byzantine Thumb then the Catholic Church.