It's intriguing that the OU is riled up about the postulation that "halachic history evidences a precedent of precluding women from serving as clergy or receiving ordination" because it "always has been normative." As Tevye said in Fiddler on the Roof, "our old ways were once new," and that plays out even in the last century. There wasn't a particular precedent when the Bais Yaakov movement was started in 1917. Remember that before the Bais Yaakov movement, girls did not receive a formal primary or secondary religious education because whatever they learned, they did so in the home. This change was revolutionary, but as the Chofetz Chaim pointed out in his ruling, it was necessary. It wasn't until the 1970s that Talmud was formally taught to women in a post-secondary setting. There was a time when women studying Talmud was forbidden. The bat mitzvah did not make its debut in the Orthodox world until the latter part of the 20th century. Even the position of yoetzet halacha, who is a female authority figure who can actually render a halachic ruling in the context of taharat mishpacha (family purity laws) and ironically has more halachic authority than a Maharat in terms of making rulings, was only created within the last few years.
Those who are against the idea of female clergy base their opposition on strict gender roles between what is male and what is female. It is the idea upon which the OU bases its "halachic ethos." The changes regarding the role of women in Judaism that were mentioned in the previous paragraph were significant changes because it not only signifies that the role of gender is not absolute in the Orthodox world, but that the Orthodox world is capable of adapting such changes. As a matter of fact, the OU does implicitly acknowledge to a certain degree that gender roles can at least theoretically change:
"The existence of female scholars throughout the history of our nation is, in our understanding, ample proof that the notion of semikha for women was conceivable. However, a continuing mesorah existed that dictated against it. We find it implausible to say that the question of female ordination has never presented itself throughout the history of our mesorah."
I can also go into how strict gender binary doesn't exist in Judaism, at least as starkly as naysayers opine. One example is with the prohibition on men wearing women's clothing, and vice versa (Deuteronomy 22:5). Not even that biblical prohibition is an absolute. If a man wears a skirt, it is prohibited because it's women's clothing. But if a man wears a kilt, which is a skirt-type garment that is very, very similar to a skirt, it's permitted. Why? Because what constitutes as "gender-bending" is baed on societal norms. Additionally, the Talmud mentions multiple times two categories of people that do not neatly fit into either male or female categories. The first is one who has male and female characteristics, or the androgynous (אנדרוגינוס). The second is the individual who is neither clearly male or female, what is known as the tumtum (טומטום). Even if you want to downplay these categories as exceptions, it does not negate the fact that the Talmudic rabbis were able to deal with a world without a black-and-white view on gender roles.
What's even better is that we do not need to look at changes made in the 20th century or Talmudic categories to see women have strong, communal roles. The Rabbis believed that Sarah had a stronger level of prophecy than her husband, Abraham (Rashi Breshit 21:12). The wife of Manoah, although unnamed, is considered to be closer to G-d than her husband (Judges 13:8-11; 13:22-23). The same goes for the unnamed Shunamite woman (II Kings 4:8-10; 4:22-23). Devorah the prophetess judged the people Israel (Gittin 88b, Baba Kamma 15a, Niddah 50a). Miriam and Hannah were also prophetesses in the Bible. Even without going into post-Talmudic texts, we can see that precedent is set for women to teach and instruct.
We can get into the legal arguments, such as the idea of communal authority (serarah) not applying when the community voluntarily accepts the person as its leader (Moshe Feinstein, Igrot Moshe, Yor'eh De'ah 4:26), as is with clergy. You can read the arguments for (also see here) and against female clergy for yourself, but at the end of the day, I believe this issue is much more about sociological issues than legal issues.
Is the Orthodox world ready for women to take on such a leadership role? What effects, both good and bad, does such a change have not only in the individual synagogue, but in the greater Orthodox world? Is the fact that a Maharat does not formally sit on a beit din, does not count for a minyan, or does not lead services enough for more religiously conservative Orthodox synagogues, or is the mere existence of female clergy divisive enough to the point where even Haredim or Centrist Orthodox Jews meeting part of the way is too unconscionable? Another way to frame that last question: is this issue irreconcilable to the point of a schism, or can there be a way for the Orthodox Left and the rest of Orthodoxy to co-exist? Was this divide inevitable, regardless of whether female clergy were ordained or not?
These are questions I cannot answer for certain because I do not have the clairvoyance to do so, nor can I dictate how recalcitrant centrist and Haredi rabbis will be on the issue. What I can say is that for those who bemoan the existence of female clergy, I dare you to either speak with Orthodox female clergy or go to a service with a Maharat present to experience it for yourself. I can tell you from having a Maharat at my own synagogue that the fears are decidedly overblown and unfounded. This is not simply a matter of the Maharat being an inspiration for girls and women to want to be more Torah-observant. The whole point of a Maharat is to teach Torah and Avodat Hashem, which she does. I would contend that a Maharat is actually better than a rebbetzin: a rebbetzin gets the position vis-à-vis the nepotism of being the rabbi's wife. A rebbetzin may or may not get the hang of it over time. A Maharat goes through multiple years of halachic training that includes laws on tzniut, as well as pastoral training, which makes her more capable and competent to handle the day-to-day operations. What's more is that certain people will be more comfortable consulting with female clergy than with male clergy on certain halachic questions. Depriving both women of the opportunity to serve the Jewish community and congregants of the contributions that female clergy can offer is a disservice. Another disservice is the OU trying to ban such proliferation while using the slippery slope fallacy or a fanciful version of the argumentum ad antiquitatem, instead of talking with a Maharat or congregants of a Maharat to better understand the issue before rendering a ruling. The fact that the OU did not take its own advice of "go and see what the people are doing (Eruvin 14b)," which the OU cited in its own response, shows how divorced the OU's decision is from observable reality and changing trends.
This is not the first time the OU has made such a controversial ruling regarding gender. A similar phenomenon happened with the mechitzah in the mid-20th century. At this time, there were a significant number of synagogues that were not using the the mechitzah. However, the OU pressured Orthodox synagogues to make a mechitzah contingent upon OU membership. Who knows how the Orthodox world would have evolved in terms of gender roles if the OU did not exert such pressure? Maybe the mechitzah would have become a thing in the past for all synagogues except the most Haredi. Maybe the divisiveness on gender issues would have caused a schism sooner. Maybe the OU's ruling on the mechitzah was merely superfluous. We'll never know, but it does seem that the OU thinks that it can repeat history. However, what the OU might not realize is that much to its chagrin, the Jewish world is more influenced by the greater world than it can imagine. In secular society, the role of women has changed, and that has spilled over even into the Orthodox world. How one conceptualizes gender has changed in the past half-century (especially with the women's rights movement), and if the OU thinks it doesn't have bearing with regards to female clergy, it is sorely mistaken, especially given that there is a obvious and growing demand for female clergy. The divisiveness does not ultimately from those synagogues who want female clergy, but from the OU declaring by fiat what constitutes as Orthodoxy, which only serves to act as a wedge by two groups of Orthodox Jews that should be working more collaboratively instead of perpetuating in-fighting. Such declarations do not resolve complex issues in the Orthodox world, but exist to exacerbate the already-existing tension.
What can be concluded here is that Judaism not only allows for women to take roles of teaching and instruction, but even more importantly, Judaism can handle a world in which gender roles do not exist in absolutes. Yes, there will be challenges to make sure that it doesn't turn into egalitarianism or that the divide between genders is completely lost. And yes, the Jewish tradition teaches us to be mindful of gender differences, even if the reminders are symbolic in nature. However, Judaism has been able to withstand changes to gender roles that were considered revolutionary at the time, and I think that it is able to do so again with female clergy.