The only requirement for membership in AA is a desire to quit drinking. In the BB, it says that "we came to believe" that a "power greater than ourselves" can restore us to sanity.
There are a million reasons the alcoholic mind will justify drinking- and that includes not giving a chance to a program that works for a whole lot of people.
To me, getting hung up on the "God thing" or whether or not there is anything beyond ourselves that can lead and guide us in sobriety is one of these excuses. Some people consider the program itself their HP . . . some people never "get past" step one- powerlessness over alcohol and acceptance of this- and stay sober.
Bottom line - I could have continued objecting to about anything (for me, Believing in God was already my known, but other things took time to accept- like step one) .... and I see a whole lot of people living the kind of lives I want and I'm doing a good job at that myself, I believe with the help of my higher power.