The 9th Circuit Court of Appeal has held that AA is a religious organization and requiring a person to attend AA would violate the person's religious rights.
WA statutes do not specifically require a defendant to attend AA. WA does require the defendant to attend treatment programs.
There likely are programs that do not have religious components. You just have to look around and ask the court to approve your treatment under those programs.
It is unlikely that the court is ordering you to attend AA to expose you to religion. It is just that AA is widely established and easy to attend for most defendants. I am sure there are plenty of atheist drunks just as there are plenty of religious drunks. You just have to do the research to find the places where you can obtain treatment.
If you don't believe you don't believe. Go through the program and do all that you can to understand your problem, because if you are seeking a DP you have a problem with substance abuse. You need to dig deep and understand where your inner fortitude will come? Why do you want to quit? Will it be for others, family, friends, etc? Will it be for yourself alone? This is your program and I encourage you to really try and stop drinking. It will improve your life and the life of those around you. Your belief or lack of it shouldn't stop you from taking advantage of the programs available to you through a DP, to improve your life and save you from jail. Good Luck
A first amendment violation would be difficult to prove unless the religious dogma is overt. Generally they refer to Higher Power rather than "god." I know some people who think of "society" or even "the court" as the Higher Power The Higher Power doesn't need to be a religious entity.
Treatment agencies generally work with people of all faiths, and I am certain that all of them have worked with clients who do not have any faith in any religion. They may actually be fairly accommodating of atheists. Look around and try to find a good treatment agency that is at least accepting of your rational point of view.
Lastly, I assume that you have carefully thought this through, but if you do not have an attorney I would strongly recommend at least consulting with a criminal defense attorney before going through with the deferred prosecution. I am certain that there are attorneys in your area who would provide a free consultation regarding your case. If you want to do treatment, fine, but you can do that on your own without the onerous burden that a deferred prosecution can present.