Leaving aside the issue of serving as a dayan, it is obvious to me that women rabbis are coming to Modern Orthodoxy, even if the powers that be are standing firmly against it. Yet they have already let the genie out of the bottle. By sanctioning advanced Torah study for women, there is no question that the time will come when there will be women scholars of halakhah who are able to decide issues of Jewish law. The notion that a woman who has the knowledge can “poskin” is not really controversial, and has been acknowledged by many haredi writers as well. Very few rabbis are poskim, but every posek is by definition a “rabbi”, whether he, or she, has received ordination or not. So when we have women who are answering difficult questions of Jewish law, they will be “rabbis”, and no declarations by the RCA or the Agudah will be able to change matters. I am not talking about pulpit rabbis, as this position has its own dynamic and for practical reasons may indeed not be suitable for a woman. Yet as we all know, very few rabbis function in a pulpit setting, and much fewer will ever serve as a dayan on a beit din.
The reason why the issue of ordaining women has been so problematic is because the Orthodox community is simply not ready for it. Yet when women will achieve the level of scholarship that I refer to, and are already deciding matters of halakhah, then their “ordination” will not be regarded as at all controversial in the Modern Orthodox world, and will be seen as a natural progression. People will respond to this no differently than how they responded to the creation of advanced Torah institutes for women. Since women were already being taught Talmud, the creation of these institutes was a natural step.
Marc B. Shapiro, “Answers to Quiz Questions and Other Comments, part 2”, The Seforim Blog (25 March 2012) {http://seforim.blogspot.com/2012/03/answers-to-quiz-questions-and-other.html}