I am confused as to what is permitted and prohibited in Judaism. Who speaks for Judaism? Who has this authority? Why are there different Judaisms, orthodox, conservative, reformist, caraites? Is Judaism today the same as Christianity with its various aspects, with the Orthodox being seen as if it were the Catholic Church and all the others as reformers and heretics for not following tradition like the Karaites? In short, who has the last word in Judaism? They say that Judaism is diverse, in what sense?
I would like to offer a (potential) answer to the second question:
Why are there different Judaisms, orthodox, conservative, reformist, caraites? Is Judaism today the same as Christianity with its various aspects, with the Orthodox being seen as if it were the Catholic Church and all the others as reformers and heretics for not following tradition like the Karaites
Following the victory over the Greek empire, as is told with regard to the Chanukah-story, "there began a dispute over the interpretation of the commandments of the Pentateuch concerning which many of the scholars held varying opinions.", as explained by Gershom Bader.
Out of these groups, there emerged so to speak three movements, with each three main tendencies. The movements were: the Pharisees, the Saducees and the Essenes.
There are many differences between these three parties, but the main difference between the Pharisees, and the Saducees is, according to Bader:
The primary difference between the Sadducees and the Pharisees consisted in that the Sadducees rejected the oral law which was accepted by the Pharisees. They maintained that only the written law of the Torah was binding upon men. In rejecting the traditions of the Pharisees, they refused to believe in the resurrection of the dead, which is not explicitly promised in the Torah. They ridiculed the Pharisees for the latter’s belief in the immortality of the soul and in a life after death and made fun of the notion that the souls of the pious will rest under the throne of glory. Another subject of their humor was the Pharisees’ readiness to endure suffering in the hope of being rewarded in life to come.
Furthermore, in the US, today, there are three major movements of Judaism: Reform, Conservative, and Orthodox.
Reform Judaism does not believe that the Torah was written by God. The movement accepts the critical theory of Biblical authorship: that the Bible was written by separate sources and redacted together. Reform Jews do not believe in observance of commandments as such, but they retain much of the values and ethics of Judaism, along with some of the practices and the culture. The original, basic tenets of Reform Judaism in the USA were set down in the Pittsburgh Platform. Many non-observant, nominal, and/or agnostic Jews identify themselves as Reform simply because Reform is the most liberal movement, but that is not really a fair reflection on the movement as a whole. There are about 800 Reform synagogues in the US with approximately 2 million members. For more information about Reform Judaism, see The Union for Reform Judaism.
Conservative Judaism grew out of the tension between Orthodoxy and Reform. It was formally organized as the United Synagogue of Conservative Judaism by Dr. Solomon Schechter in 1913, although its roots in the Jewish Theological Seminary of America stretch back into the 1880s. Conservative Judaism generally accepts the binding nature of halakhah, but believes that the Law should change and adapt, absorbing aspects of the predominant culture while remaining true to Judaism's values. In our experience, there is a great deal of variation among Conservative synagogues. Some are indistinguishable from Reform, except that they use more Hebrew; others are practically Orthodox, except that men and women sit together. Most are very traditional in substance, if not always in form. There are an estimated 800 Conservative synagogues in the US today with approximately 1.3 million members.
Orthodoxy is actually made up of several different groups. It includes the modern Orthodox, who have largely integrated into modern society while maintaining observance of halakhah (Jewish Law), the Chasidim, who live separately and dress distinctively (commonly referred to in the media as the "ultra-Orthodox"), and the Yeshivish Orthodox, who are neither Chasidic nor modern. The Orthodox movements are all very similar in belief, and the differences are difficult for anyone who is not Orthodox to understand. They all believe that God gave Moses the whole Torah at Mount Sinai. The "whole Torah" includes both the Written Torah (the first five books of the Bible) and the Oral Torah, an oral tradition interpreting and explaining the Written Torah. They believe that the Torah is true, that it has come down to us intact and unchanged. They believe that the Torah contains 613 mitzvot binding upon Jews but not upon non-Jews. The Judaism 101 web site (the starting point of this "site within a site") was written primarily from the Orthodox point of view. It has been estimated that there are 1200 Orthodox synagogues in the US today with a total of approximately 1 million members.
I do not know very much about the Catholic Church, but this article says:
It teaches that revelation has one common source, G-d, and two distinct modes of transmission: Sacred Scripture and Sacred Tradition
This seems to connect to our idea what the Talmud is and what role our tradition, from Sinai, is. Please correct me if I'm wrong.
The Torah says כל ישראל ערבים זה בזה - All of Israel are responsible for one another. This shines through your sincere question, which is almost saying "hold on, I expect that Jews should be teaching the same thing, it doesn't make any sense that there are all these differences". Beautiful.
משֶׁה קִבֵּל תּוֹרָה מִסִּינַי, וּמְסָרָהּ לִיהוֹשֻׁעַ, וִיהוֹשֻׁעַ לִזְקֵנִים, וּזְקֵנִים לִנְבִיאִים, וּנְבִיאִים מְסָרוּהָ לְאַנְשֵׁי כְנֶסֶת הַגְּדוֹלָה Moses received the Torah at Sinai and transmitted it to Joshua, Joshua to the elders, and the elders to the prophets, and the prophets to the Men of the Great Assembly.
The Torah was given at Har Sinai in the year 2448 of creation, 3335 years ago. This was effectively the "start" of Judaism, the cannon, the OG. Clearly, any ideology that tries to change what was received and transmitted from Sinai is not Torah. Here, we are not talking about the Written Torah, but the Oral Torah.
As the above Mishna lays out, it has been handed down in a chain of tradition. In fact, the Torah gives us a mitzva (see Sefer Hamitzvot Negative Mitzva 312 and Positive Mitzva 174) to explicitly to listen to the Torah authority of the generation:
עַל־פִּ֨י הַתּוֹרָ֜ה אֲשֶׁ֣ר יוֹר֗וּךָ וְעַל־הַמִּשְׁפָּ֛ט אֲשֶׁר־יֹאמְר֥וּ לְךָ֖ תַּעֲשֶׂ֑ה לֹ֣א תָס֗וּר מִן־הַדָּבָ֛ר אֲשֶׁר־יַגִּ֥ידֽוּ לְךָ֖ יָמִ֥ין וּשְׂמֹֽאל׃ You shall act in accordance with the instructions given you and the ruling handed down to you; you must not deviate from the verdict that they announce to you either to the right or to the left.
From this the commentators learn that there will always be an authority in Oral Torah matters, starting with the Supreme Sanhedrin in Jerusalem See Mishne Torah Rebels 1. In fact, I strongly recommend reading all the links I have provided in detail to get a good handle on the logic behind this.
There have been many factions that have tried to reject or deeply corrupt the Oral Torah (almost always due to politics). The vast majority of them completely disappear after not many generations, which shows how important the Oral Torah is. Even the Karaites didn't get any new authorized members for 500+ years, and are today a relatively tiny movement.
Nowadays, due to the haskala, and the general rise of secularism since the enlightenment, there have arisen several ideologies that secularise Torah, and unlike the Karaites, they are all very large. Rav Dovid Gottlieb clarifies this subject by stating that you can view most of modern Jewish movements as falling into two categories: traditionalists and non-traditionalists. These movements are the latter. They all, in some way, reject some of the tradition, either that the Torah is Divine, or even that God exists! They all start from some level of a modern, secular argument and work it backwards into the tradition, and therefore upend the tradition. Of course, they will all claim they are the "last word" in Jewish matters, but you have to decide that for yourself. They will all happily admit that their practice and philosophy is modern, new, and a change from what was the norm for thousands of years.
It should be abundantly obvious, these two types of break-away, those that reject Oral Torah, and those that reject tradition, represent the "deviations to the right, and to the left".
It shines through your question, as well as my general dealings with you on this site, if I may, that you are someone who expects Judaism to be a tradition from Sinai, unbroken, and undivided, and you accept Torah was written by God directly. Therefore, the answer to you is that the authority in Jewish matters comes from the traditional category. There are many, including the Litvish, Sefaradim, Chassidim, Modern Orthodox... Certainly, Conservative, Reform and Reconstructionist Jews will claim that I am being biased, and bringing only sources from my own "camp" to which I say, fair enough, they are welcome to answer the question as well, please decide for yourself.
It's a sad reality that today, not all Jews follow or speak for authentic, traditional, unchanged Torah Judaism, if any Judaism at all, so I understand why it is confusing as an outsider and I appreciate the question. As Isaiah states in his chapter 10, only a remnant of Torah-keeping Jews will arrive in the end times. We have seen this to be very clearly true, those that reject the tradition in any way have (almost) all been lost to history, their staying power simply doesn't exist. That's also the case for the modern movements, within a generation or two, the children find zero reason to continue the tradition and are also lost, and all are suffering some form of crisis. Orthodox Jews, on the other hand, are growing exponentially...
The Orthodox select their "leaders" in a very organic, non-formalised way. The Sages of the generation are geniuses, who have demonstrated tremendous breadth and depth of understanding of all areas of Torah (and, in the same way as any mastery, fellow masters are the ones who are able to recognise this, after the public has initially picked them up), spectacular character and deeds, and sometimes the fact they are descended from previous great leaders is of importance.
The "final say" is also more organic than you might realise. The various Orthodox "camps" all have mutual respect in "legitimacy" (notwithstanding inevitable politics), even if their own particular leaders reach different conclusions from one another. This is something that is very possible and correct in Judaism, but the reasons for that are outside the scope of this answer.