There are separate questions being raised here, and they should not be confused.
1 – The philosophy of 12-step programs is accused of being of Yoshke origin. Should that be acceptable or permitted to a Torah Jew?
The premise is incorrect. Just read the Big Book, and you will not find a single reference that recommends or suggests anything about any specific religion. The wording, when referring to G-d, is always qualified with the phrase “as we understood Him”. Religion is not meaningful to 12 step programs at all. What they do push for is “spirituality”, something that we Jews need to make part of our Yiddishkeit. “Judaism” without spirituality is not compatible with Torah. There are a great many articles and other publications that draw distinct parallels between Torah and Mussar and the codified 12 steps. Books by Rabbi A. Twerski are packed with proofs of this, and others have also published on this widely.
Some years ago, there was psak from Rav Elyashiv ZT”L that was disseminated everywhere that 12-step programs should be considered avodah zoroh, and that it is ossur to attend their meetings. It turned out that he was misled by one or more individuals. Several frum therapists brought material to him that refuted the opinions of the original trouble makers. He issued a psak that rescinded the earlier issur.
Much is written about the history and origins of AA. It is not religion, nor based on any religion.
2 – Can information specific to other religions be spread in the rooms of 12 step programs?
Yes, it certainly can. And it can be circulated in the streets, the supermarkets, and in publications. The rooms of 12 step programs are composed of imperfect people who are on a mission to improve themselves. The program does not advocate the giving of advice, and even the “leaders” of groups are volunteers who are also recovering from addiction, not professionals. Suggestions are to be couched in the frame of, “This was helpful for me,” and not as recommendations. Could one benefit from hearing that a recovering person was helped by connecting to his faith, even if not Jewish? Of course. The greatest of our tzaddikim recognized that the truly observant goy is not the same creature as the thugs in the street, not the terrorists and criminals that hurt us. The program teaches to “Take what you need and leave the rest”. We should recognize this as תוכו אכל קליפתו זרק.
Spreading religious literature at a 12 step meeting is against the program. So is relapse. But it happens. And if anyone wants to get riled up about the imperfections of the program, save the energy for those who attend our shuls, talk through davening and kriyas haTorah, get wasted in Kiddush clubs, and limit their observance of Torah to wherever they are seen by others. Stopping these disgraces to our מקדשי מעט and restoring observance of Torah law to בסתר ובגלוי will do wonders for us and our children.