There is of course the solution offered above. It's interesting, but it can become extremely tricky to play, especially considering IC->OOC bleedovers. Even if other characters do not know about it, some of their players will. Be they applying a strict OOC/IC separation or not, the bleedover will occur, probably very limited and harmless in the first case, and not so much in the second one.
Also, something I have learned over the years of Eve RP is that a lot of players are really quick to jump on appearances and what looks to be. Half of the people will immediately fall for the mask a character wears. I have had a great time playing with that over time, making people immediately assume something about my characters and counting on it, and when it inevitably happens because they are looking to put people in properly labelled boxes, they are ready to face a very nasty surprise. If there is something that will confuse people to incredible heights, it is to deal with characters that are really hard to properly discern. Every time they want to counter argue something against such a character, they have to assume at least a bit of his/her positions to make a point, and since your character is elusive, they often completely miss the point and then gets completely puzzled as why the answer that your character gave them is completely not what they expected. It is especially sharp against characters that see the world in black and white. It threatens the very core of their view of the universe.
With that in mind, I think you can have a lot of fun if you play it correctly. It also implies to correctly hide the true beliefs of your character, and in my case I had to create a shitload of different layers in her ideals that can literally be peeled like an onion, the outside mask, the outside beliefs, the familiar mask, the familiar beliefs, the intimate beliefs, etc. Tbh it's the only thing that has kept her alive when she had to face some of the most conservative of the loyalist bloc (edit : aside from the fact that you will have to prove even more that you are a loyalist and still give your life for your empire, I also have 3 years of FW as well as 1-2 years of CVA to back up my claims for example).
So, that said, there is what was proposed above, playing a true amarrian atheist. In my case I chose something less radical. I happen to believe that the Amarr are like all the 3 other empires a modern empire, not a medieval one. It's not the W40K Imperium either. Which also makes me say that what is the most interesting in my eyes in fleshing out the Amarr Empire is to get out of the usual spanish inquisition trope and see what a truly, deeply religious superpower would be in a future setting. Most cultures and societies tend to calm down and enlighten over time, not that it's always true, mind you, but they become more and more subtle at the very least. With that in mind I think that a side of the Amarr Empire that is underplayed is their enlightened, scholarly side. It was also mentioned somewhere that after Vak'Atioth the Amarr started to put everything into question and went then through an age of enlightement under Heideran VII's reign. I would expect that after all these centuries of peace and self introspection they would have seen religious debate, or at least discussions, forums, to become rather popular. There is also the statement that most Houses have developed their own ideals and customs and have gotten more and more separated on that particular point. The most liberal of them can probably offer a lot. When I see the standard Amarr orthodox characters/organization trying to bully other amarrians with different beliefs, i'm sad to see that they do not seem to know how to react or that their world conception is also a valid one (not speaking about the "lolol I loathe the Amarrian faith and will join the TLF").
Eventually I chose to still play a believer, but not in the religion itself. The scriptures can be considered as a collection of philosophical thoughts, spiritual thoughts, science things, etc. The core of the Amarr religion is not extremely religious. Even God can be deconstructed into something very literal that can fit a more atheist approach. Eventually one could say that my character is an atheist - and she probably comes very close to that - but she still believes in most of what is scripture, in her own interpretation. I would also expect a lot of Amarrian scientists to have a rather... pragmatic view of the Faith (like my character), but that doesnt mean that they are atheists. Some maybe, but even IRL the last I checked there is like 50% believers in the scientific community.
Please, don't conform like everybody to the same Amarrian trope that came from PIE. Inc and the likes. They are the beacon of what the Amarrian orthodox is, they set the standard, but i'm a little sad every time someone wants to play something different that they eventually give up because they are alone and roflstomped on the IGS.