There's actually a lot of evidence to suggest the opposite, that the Maesters are a secular organization. There's a very good theory that's been very well-supported that suggests that the only reason the Maesters support the Faith of the Seven at all is because they think it's truly false and has no power behind it, thus they can use it to manipulate and combat magic and other supernatural happenings. Think about it: the Faith of the Seven is the only religion in the entirety of the series that has not had a display of some supernatural happenings. The Many-Faced God = Faceless Men and however they do that. Old Gods = Greenseers and Wargs. R'hollr = fire magic, telling the future, resurrecting Berric Dondarrion, and Mel surviving poison and not needing to eat. But we've had nothing like that from the Seven. No dreams of the Mother telling someone what to do, no knight imbued with great strength from the Warrior, nothing. And this is the religion that the Maesters seem the most okay with.

Doesn't that seem odd? There's been a lot of implication that the Maesters are trying to fight the return of magic to the world, and being able to mobilize followers of The Seven against the other religions (which do have magic or something behind them) knowing that The Seven actually carries no magic or supernatural element. The only things you're pointing at that suggests Maesters are associated with the Faith are Cressen being upset about burning the Idols and Pycelle mentioning things about trials by combat and such. Since we have a POV from Cressen, you can go back and recall that he wasn't terribly concerned with Stannis changing religions, he was only concerned with the fact that it showed how much overt control Mel had over him. He didn't take any action against her until she suggested that Stannis kill Renly and Stannis didn't reject that. And Pycelle is only mentioning those things because they're technically law, so of course he'd speak up. I suggest you read through these threads, they go into a lot of information that contradicts the Maesters being religious at all.