I have been asked this question before and what I have told others is that AA and Alanon are simply the door that people step through and allow each person to discover their own spiritual path to what they believe. It's a spiritual kindergarten and I have known atheists who became pastors and others who don't believe in God and still do not as well as a lot in between.
AA and Alanon roots are solidly basic Christianity and it's founders found that the principles worked and kept them sober and rewrote them into the steps we now all know. They are universal principles that have been shown to be very effective.
The reason is that we are hardwired to be spiritual beings and our brains actually fire when we have a belief system that there is something bigger and beyond us.
Now... have we evolved to respond to gazing at the stars and the incredible universe or did a God actually hardwire us for us to search and find Him?
Ahhhhh... the big question that each of us must discover for ourselves. But a fascinating study that I have long enjoyed in my life that started out as an atheist... a militant angry one at that! My father the psycho A raised me to hate those who were stupid enough to believe in a God... especially those who knocked on our door. He would invite them in and terrorize them and actually get a gun. We were the only house in our neighborhood that were on Jehovah Witness no contact lists!
So... no matter what we believe and there is a LOT of different belief systems (33,000 + Christian denominations alone) something is TRUE. And if you believe it is true your brain will respond to that and help you become a happier person in your belief system. Now everything thinks THEY have the corner on the truth and the front row of heaven is reserved for them and those who believe like them so sorting this out takes some work! But it is worth it because it is important!
Secondly, the program we follow is one of community and being there for one another in a supportive role even in our diversity of belief systems. The beauty of this that you can find a community of Alanon that you feel comfortable in as many are much more secular than others. When we are comfortable in our belief system you don't have to be intimidated in what others believe and can still share in community with them.
Maybe you could start a spiritual investigative journey and along the way you may embrace your own philosophy and lose the fear you have from a past traumatic experience.
In my own experience my spiritual journey is the most important one in my life and the most enriching and empowering! And if a JW shows up at my door I can be tolerant and kind instead of evil as my father taught me! And I am no longer an atheist and have a personal belief system that my dad would hate!