For some reason I really don’t enjoy writing about this topic so I’m going to make it brief. Some more (final?) thoughts on psak and hashkafa:
1) Shapiro writes, “I have said, and I repeat now, that no rishonim that I am aware of, and certainly not Rambam, believed that Principles of Faith can be decided in a halakhic fashion.” I’m really confused by this one: aren’t there dinim that tell us who is a min? Wasn’t that the whole point of the 13 ikkarim?
2) I assume Shapiro meant the more narrow claim that halacha cannot decide between different shitos of theology. His proof: since Rishonim critique the Rambam as having rejected views which were at one time espoused by Chachamim without considering that the Rambam chose to pasken against those views, QED psak is impossible. I don’t follow the logic here. These Rishonim assumed that an ikar must be axiomatic, not something over which there was different views (see Sefer haIkkarim 1:3). Even Rishonim like the Sefer haIkarim who do not have substantive disagreement with the Rambam still take issue with his labeling matters upon which there was disagreement as ikkarim. While Shapiro highlights these views, he seems to forget that the Rambam himself obviously disagreed with them! And, as Shapiro himself demonstrates in the first chapter of his book, most achronim accept the Rambam’s 13 ikkarim despite the critique leveled against them. This is no different than any other area where Rishonim stake out different position and tradition has accepted one view over the other, namely the view of the Rambam that labels an ikar as a significant belief even though views to the contrary may have once existed. Note as well that Rishonim like Albo do not disagree with the notion of deciding which beliefs are correct (e.g. Albo assumes one must believe in mashiach even though a Rabbi Hillel in the gemara did not hold of such a belief) - they disagree only with the semantic issue of labelling these beliefs as ikkarim.
3) There is a recurring claim in comments that belief is different than action, but no one has gone beyond stating this as a truism to adequately explain why or what source would indicate this. Furthermore, and this is a critical point: isn’t every statement about what to do implicitly a statement about belief? One cannot don Rashi’s tefillin every morning and simultaneously believe that Rabeinu Tam was correct in how the parshiyos should be ordered. If you put on Rashi’s tefillin it is because you believe that such an act fulfills the will of G-d. Actions are just expressions of our beliefs, So why the distinction?
4) With regards to paskening on a “metziyus”, e.g. as raised in the comments, how can we use the rules of halacha to determine the historical truth of who wrote the last 8 verses of the Torah. Answer: we are not defining a metziyus, but deciding that one version of the mesorah is more authentic than another version. For example, if most historians date the birth of Ploni to July 4 and one historian claims his birth was July 5, assuming that Ploni was born on July 4 is simply choosing to accept the consensus view as a good indicator of what is factually accurate. The Mahartz Chiyus explains Tos, in Yevamos (to finally get back to that!) as properly claiming Malachi was Ezra because the targum proves that version of the mesorah more reliable.
5) None of the places in Peirush haMishna where the Rambam says he cannot pasken deal with necessary beliefs. I don’t see why these statement have any bearing on ikkarei emunah, which are necessary beliefs - you can't just throw up your hands and say you have no idea, because by definition these are required beliefs. Nor do these statements contradict Tos, because Tosfos needed to decide a historical question for the sake of bolstering a halachic argument. Where there are equally valid sevaros and claims and there is no pressing need to choose one mesorah over the other, or where the debate is of such a nature that one cannot choose one over the other, why should one do so? That's all the Rambam was saying. Why has this simply rule become a mantra among those who want to claim halacha cannot decide ikkarim?