Former addict of opiates here, I've attended a lot of AA/NA meetings in the long ago past (8+ years ago).
They may not claim to be religious, but every single step mirrors the idea that you are to give up to a 'higher power' and to 'faithfully' follow the steps...etc...etc.
It's as religious as it can be while still trying to claim otherwise...in reality its a thin veneer for a truly religious/faith based system. It's got religion all up in its business...the claim to irreligiosity is a fig leaf, in my experience.
I also truly hated their angle of making you feel like you are forever a victim/failure to addiction...that is not how you promote a prosperous and good outlook on life. In fact it's a good way to make you feel like shit and use again.
What I learned later on is that yes, you can let your past be your past...no I don't want to take opiates...but I also am no longer an 'addict'. I am me, and I don't consume addictive pills anymore.
Also, as an anecdote, over 8 years clean here...and that didn't happen till I gave up on AA/NA.
Edit: After reading a few more messages, this one in particular was on point and stated things better than I can: https://news.ycombinator.com/item?id=22553896