When discussing which beliefs are heretical to orthodox Judaism the phrase "there is no shulchan aruch on deos-beliefs" comes up often. I would like to know why this is the case. Why can there not be a single set of canonized, agreed upon beliefs which if you don't hold, l'halacha you are a kofer/apikorus/min?
I think the premise of this question is mistaken, for a few reasons:
Rabbi Hirsch wrote a pamphlet as an answer against one that was written by a Reformer. It is called Religion Allied With Progress, found in the collected writings volume 6 starting on page 107.
This excerpt begins on page 112. I have bold typed the main point I'm bringing at the end.
The rabbinical authorities ousted the proclamation of articles of faith for Judaism not because they believed that Judaism has no basic tenets but because they regarded every aspect of Judaism as basic. Judaism, they held, knows neither thirteen articles of faith, nor three. In Judaism, every commandment and every prohibition constitutes a fundamental religious principle and anyone who dies the validity of even one of the 613 commandments and prohibitions thereby places himself outside the pale of Judaism.
Page 113. Indeed, Maimonides himself would have been the last to claim that the acceptance of his thirteen so-called articles of faith made a Jew a Jew, or even that these tenets contain the essence of Judaism. Pirush hamishnayos on Chelek yisod 8 and 9 he himself sharply condemns any attempt to divide the laws of the Torah into essential and non-essential categories. He writes etc.
There is complete agreement among all the Rabbinical authorities in this respect; hence there was nothing inherently wrong in enumerating basic tenets of Judaism as Maimonides did. However, there was reason to fear that such enumeration might be misinterpreted by the ignorant, by the wicked or by unlearned authors of pamphlets, and that is why some authorities were rightly opposed to any attempt to schematize Judaism.
The Rambam's 13 principles of faith are fundamental beliefs. They are said to be based on the 10th perek in Sanhedrin which lists things that "אין להם חלק לעולם הבא" e.g. non-believers of resurrection of the dead, non-believers of Torah from heaven and apikorus. The remainder of the perek lists more.
The Rambam repeatedly wrote that we can't make conclusive/authoritative on matters of faith/hashkafa:
"And I've already written several times, that when there's a dispute between the sages in arguments of faith, the purpose/end is not to [establish] practice- since we don't say the halacha is like so-and-so and against Ben-Azai" (Commentary on the Mishnah, Sotah 3:5)
"All disputes amongst the sages that have no practical application, but are only in matters of faith, there's no position to decide halacha according to one of them" (Commentary on the Mishnah, Sanhedrin, Perek Chelek)
(Commentary on the Mishnah, Shavuot 1:4)
(ספר המצות, לא תעשה קל"ג)
(מאמר תחיית המתים)