A desire to stop drinking is the only requirement for AA membership.
However, for success in AA, certain personal characteristics are required, more often than not. If an individual does not display these, they can be learned, but they had better be learned fast.
(1) The ability to follow instructions regardless of what one thinks or feels about the instructions
As Clancy says, Step Three in practice means 'taking actions you do not believe in because people who are doing better than you are suggesting them'. It does not matter a jot whether you believe in the individual actions themselves; what matters is how well the people are following and suggesting these actions are doing. If they are doing better than you, do what they say.
(2) The willingness to be uncomfortable
Alcoholics who come into recovery are typically emotionally childish. They want lollipops and puppies and freedom from any pain or discomfort whatsoever. If this failing is not broken, and broken fast, recovery likely won't 'take'. The core of the alcoholic's (and addict's) pattern is this: short-term gain plus long-term pain over short-term pain plus long-term gain. To get and stay sober, one is simply going to have to put up with sometimes significant doses of feeling exceptionally uncomfortable. Accept that like a grown-up, and that's most of the battle. Recovery is not for cissies.
(3) Knowing what a decision is
There are elements of the recovery process where we have to examine crucial issues: do I want to stop drinking for ever? Am I convinced that I can never drink safely again? Am I convinced I cannot do this on my own? Do I believe AA works for others, and will therefore work for me? Am I willing to go to any length? However, once this sequence of considerations culminating in a decision is complete, it must not be revisited, except deliberately in consultation with a sponsor.
The Step Three decision—to continue promptly and resolutely with the rest of the programme—is a final decision. Endlessly revisiting the foundations—the above considerations—will cause confusion and weaken resolve and may lead to relapse. If in doubt, give recovery a year, or even five years, and resolve then to re-examine the foundations. Until then, get on with it.
(4) Exercising mental discipline
The spiritual programme of action includes mental actions. There are plenty of mental actions described on pages 84 to 88 of the Big Book. In practice, this means not permitting any resentment, fear, nostalgia, fantasy, doubt, or other negative or destructive thinking. In practice, we are tempted a thousand times a day. With practice, we can turn away from such thinking promptly, with God's help, and turn to how we can contribute usefully to the day and help others. Good sponsors and spiritual advisors will be pleased to help with prayers or other readings that can be instantly applied to block unwanted trains of thought.
Sobriety cannot withstand being deliberately undermined from within by self-indulgent thinking (and the self-indulgent action that flows from it). We are not responsible for temptation arising, but we are responsible for how we respond to it.