What, if anything, do Jewish sources say about the religion practiced by King Ahasuerus and Haman? Does Jewish legend support the conjecture that they were Zoroastrian?
"Jewish sources" do not come right out and specifically state which exact religion Ahasuerus and Haman followed. However, we can read the Jewish sources, and secular historical sources, (archeology, ancient texts, modern scholarship) to try to find the best answer implied by the Jewish sources. Dr. Chaim S. Heifetz, a modern day Orthodox Jewish scholar, who has spent many years studying these sources, (both Jewish and secular), proposes this answer:
Ahasuerus and Haman, were both (most likely) Zurvan-type (idolatrous) Zoroastrians. Specifically, they would have been followers of the cult of Mithra, as promoted by the Magi (a priestly class of the Medes). This would be as opposed to Cyrus the great and Darius II (for instance) who (most likely) followed a monotheistic form of Zoroastrianism.
First, we need to understand a brief explanation of the difference between a Zurvan vs. monotheistic, Zoroastrian.
Zoroaster (or Zarathustra), who founded this Persian religion, taught a monotheistic concept. Ahura Mazda , was the one and only God of light who created everything. Humanity was to use free choice to constantly battle the temptation of being evil. This would uplift humanity, until the final battle of good vs. evil and the resurrection of the dead with the coming of Messiah. Individuals would also be judged to enter heaven or hell based on the majority of their thoughts and deeds while alive.
The evil spirit was called Ahriman. It was not a god, but rather an emanation set up by Ahura Mazda. This is similar to a Jewish Satan. or Yetzer Hara. Mithra, is mentioned in the Avesta (Zoro-A holy writ) as merely an emanation of an attribute of God.
This version of belief has not been pinpointed to a certain year, but is usually attributed to approx. the 6th century BCE (also, as far back as the 10th - 12th century BCE). In this version, evil is merely a test supplied by Ahura Mazda, so man can improve. Judaism would find this general belief to be very acceptable (as far as gentile religion goes). One can see the obvious parallels within Judaism.
However, Persia and Media became established by migration from India. Those peoples were followers of the Hindu Vedas. They had many gods and one of the main ones was Mithra. The Medes and common people led by the Magi priests, continued the old idolatrous ways. When Zoroaster made reforms, many people still needed to mix pure monotheism with idolatry. One version of Zoroastrianism was Zurvanism. Zurvan, was the neutral god of time. He created Ahura Mazda (good god) and Ahriman (evil god) as twin brothers. They fight throughout history. This kind of dualism is idolatry, and appealed more to the masses that followed the Magi and Mithra. (Later, Sassanid Persian royalty, followed Zurvanism, complete with priests (Chavarim) of the fire worship cult which had its source with the Medes.)
A follower of this kind of Zoro-A, could be happy with sacrificing to different gods. Kings could be incarnations of gods or at least high priests of certain gods like Mithra.
Seder Olam, informs us that the Jewish chronology recognizes only four Persian kings. They are Darius I the Mede, Cyrus (the Great), Ahaseurus (of Esther), and Darius II.
Isaiah 45, mentions the Persian Cyrus, as being the Messiah of G-d. In Ezra 1, Cyrus authorizes the Jews to return to Jerusalem and rebuild the temple. Cyrus is quoted as referring to the "G-d of heaven". Darius II, who takes over after Ahaseurus, (and may be the son of Esther) orders the temple to be built once again, and renews the decrees of Cyrus, in favor of the Jews.
Ahaseurus, is discussed by Seder Olam, Esther Rabbah, and the Gemara in Megillah. He is identified with a reversal of Cyrus' order to rebuild the temple. He profanes the temple vessels at his party, and dons the stolen high priest's vestments. Described as an unfit usurper to the throne, his party is explained by the sages as solidifying his reign after the first 2 years of dealing with rebellion. Interestingly, the Jewish temple's ruin means so much to him, that whenever he offers his queen (who he doesn't even know is Jewish) something, he offers her anything she wants: "until half the kingdom". The sages explain this to mean: "but don't ask me to allow the Jewish temple to be rebuilt!."
Haman, is described as wearing an idol around his neck, and wanting to be worshiped as a god. The king raises Haman up as the highest man in the realm and makes a special decree that everyone bow to him. Also, Haman slanders the Jews to Ahaseurus by saying that "If a fly falls into a Jew's wine, he removes the fly and drinks the wine...but if your majesty touches their cup, they throw it out!"
This slander is strange. The Talmud in Chulin (4b) explains that only if wine was offered to an idol, would a Jew not be able to drink it. The decree of "stam yenam" (that the mere touching of the wine renders it prohibited) was not decreed until the times right after Hillel and Shammai. This was hundreds of years after Esther. Where did Haman get this? Tosfos answer (in general, to the Gemara referring to Ahab, but I will apply it equally to Haman): that if a gentile is known to be a priest of an idol, then anything he slaughters (I assume wine touched is included) is considered automatically idolatry, and is prohibited. If Haman and Ahaseurus were incarnations of gods, or priests of Mithra, then it makes sense.
Dr. Heifetz's Theory:
Dr. Cheifetz interprets these sources to tell us that Cyrus and Darius II were monotheistic Zoroastrians, while Ahaseurus and Haman were idol worshipping Zoroastrians.
Cyrus started his success by believing in strict monotheism. Eventually, he understood the prophecy in Isaiah to be supportive of him, and made friends with the Jews. Ahaseurus, rose up against the rule of Cyrus, and took away the throne. In order to fully control the people, he needed to sway them away from the religion of Cyrus, and go back to the roots of idolatry among them. If he could make a new state religion and convince the people, he could blot out the legacy of Cyrus who he usurped. From now on, everything about Jews, monotheism, and the temple, were anti-Ahaseurus. He even married a woman from the old idolatrous royal house of Babylon and used the temple vessels. Elevating Haman, and having people deify him, was what a king would do to sway the people back to Mithra worship and following the chief Magus (Haman?). The Jewish leader Mordechai, not bowing, was indicative, that the Jews would stand in the way of religious reform, and needed to be removed.
Dr. Cheifetz also claims that a Magi usurper, overthrows the capital, after the death of Ahaseurus. This man is named Guamata in some sources. Other sources call him Hamedatha; which is the name of Haman's father! This man is soon killed. Later temples of Mithra, encouraged worship of two gods not mentioned in the past: Omanos and Anadatos. Strabo writes about them being worshiped in his city in the 1st century CE. Dr. Cheifetz feels these are corruptions of Haman and Hamedatha, two martyrs of the Mithra mystery religion.
Here is a link to an article written by Dr. Cheifetz's student Brad Aaronson (posted by Lisa (Aaronson) Liel on her website) which touches on some of these points. It was once printed in 1991, in the Jewish Action magazine.
Jewish tradition is pretty mum on the subject, as far as I've heard. The Ahasueros described in the story is driven by ego, lust, rage, and alcohol, so his religion is kind of a moot point.
There is a Jewish interpretation that Haman was wearing some sort of idol around his neck, and that's why Mordecai would not bow down to him.
But not a lot of specifics. Not really our concern, in this case.
Zoroastrianism is very clearly referenced a few centuries later, in the Talmud. (E.g. conversations about when it would be dangerous to have Sabbath candles lit "as the local non-Jewish population allows fires only in their temples on certain days"; the intentional rewording from Isaiah to the prayer books of "God who makes peace and creates evil" to "who makes peace and creates everything"; and the disqualification of a cantor whose prayer language implies there are separate gods for good and evil.)
The Chavarim mentioned in the Gemara are most likely the Zoroastrians. This we can see from their fire worship. The Gemara in Shabbos 45 mentions the issue of the Chavarim not allowing people to use fire for personal reasons.
However , the Chavarim came about during the time of Rebbi Yochanan as we find in Yevamos 63b. It seems like it was introduced or perhaps revived by the Sassanian dynasty, which is during the time of Rebbe Yochanan.