I am atheist/agnostic (depending on the definition: I am as sure as I can be of anything that no god exists, but since all our knowledge is preliminary, I can't rule out with absolute certainty that I might be wrong. I count myself atheist rather than agnostic since I have the same degree of certainty about gods as I have about well-established knowledge gained by science. Neither is absolute, but I treat it as truth in everyday life).
Towards Andrasteanism, I have a similar attitude as I have towards my culture's dominant religion. I leave it alone as long as it leaves me alone, but I will get hostile if it attempts to interfere in my life or my protagonist's life, respectively. Unfortunately, such interference is a natural aspect of functional religions, so some conflict is inevitable. My concern about DAI is that I might not be able to disassociate my protagonists from Andrasteanism. I do not expect that my atheism will be explicitly represented in the choices I can make as the Inquisitor, but I do expect from Bioware that they do not explicitly exclude atheist players from identifying with their protagonist by making them canonically positive towards Andrasteanism.
Also, my disagreement goes deeper than a mere "I don't believe in the Maker" (which alone would be pretty irrelevant), and it is with the religion, as represented by the Chant of Light, not just the Chantry and its practices. At the heart of this disagreement lies a fundamental values dissonance between myself and a central part of Andrasteanism's mythology as told through the story of the Golden City.
What is this? Well, I believe that the human drive to explore, cross the borders from the known into the unknown in order to increase our power to control our own fate (I am explicitly including the latter), that this is a virtue. Not good in a strictly moral sense - it can't be since it doesn't deal with human interaction and community - but a virtue, one of several possible cornerstones of a good life. Thus, I believe there was virtue in the ancient Magisters' attempt to reach the Golden City. This was tainted by their methods, and we can reasonably conclude that their motivations were as far from innocent or virtuous as we can imagine, but....the Chant of Light is not concerned with those. It doesn't even mention the blood sacrifice, the true evil of the Magisters. For the Chant of Light, what matters is that the attempt to reach the Golden CIty exemplifies the sin of pride. For me, if I disregard the methods as the Chant does, it exemplifies a virtuous undertaking.
On an allegorical level, the story of the Golden City presents an injunction to leave certain aspects of the world untouched by human artifice because they are fundamentally beyond our domain. I do not accept such boundaries. In my view, making these our domain is a virtuous act, if we do it responsibly. To use Christian terminology, to eat from the Tree of Knowledge was a virtuous act, and I only regret that we didn't get to eat from the Tree of Life, too, before we were caught - by an authoritarian father figure who can't accept that his children eventually grow up.
Thus, if my dislike of my culture's dominant religion parallels and reinforces my dislike of Andrasteanism, then this is because I have the same fundamental values dissonance between myself and either of them. I knew, or at least heavily suspected, that I would very much dislike Thedas' dominant religion on these grounds about 30 seconds into the intro of Dragon Age: Origins: "The Chantry teaches us that it was the pride of man that brought the darkspawn into our world" is the first sentence spoken. I have found no reason since to moderate my dislike, since a religion would be hard-pressed to find a philosophical stance more anathema to my own beliefs, and if I'm forced in any way to subscribe to it, DAI will not be my story and I will never be able to create protagonists I identify with. I do not limit myself to protagonists who believe as I do, but I must be able to play them if I want to enjoy this game as a roleplaying game as opposed to a game where I play a predefined character, where this does not matter as much.
The ME3 team told us, before ME came out, that we could roleplay against the Alliance. We could not. The DAI team told us we will not be forced to be friendly towards the Chantry and its beliefs. I just hope they're making it true this time.
Sidenote:
As a rule, I do not destroy the Sacred Ashes in DAO. They have a real power to heal beyond any other known magic, and to destroy such an immeasureably valuable and beneficial thing is against my personal ethics. It's also unbelievably petty if the only reason is that you disagree with the dominant interpretation of its origin. On the other hand, the decision to not destroy it has nothing at all to do with accepting the religion.