First, this post by /u/cleopatra_philopater should shed some light on part of your question and provide some useful sources.

What I can talk a bit more about is the practice of xwaetwadatha or xwedodah, "next-of-kin marriage" in Zoroastrianism. This is most infamous as sibling- or parent-child marriage, but the interesting thing about it is that it could also refer to first cousin marriage, which was probably the most common type of marriage (and remained so in Iran until modern times, as far as I know). The first appearance of the Avestan term xwaetwadatha is in Yasna 12.9, the closing line of the Zoroastrian creed, but it reads like a late-ish insertion and is usually bracketed:

I pledge myself to the Mazdayasnian religion, which causes the attack to be put off and weapons put down; [which upholds khvaetvadatha], Asha-endowed; which of all religions that exist or shall be, is the greatest, the best, and the most beautiful: Ahuric, Zoroastrian. I ascribe all good to Ahura Mazda. This is the creed of the Mazdayasnian religion.

While Yasna 12 probably dates to around 1000 BC, the insertion could well date to as late as the Arsacid (Parthian) era, though I would say Achaemenid era is more likely at face value (simply because that's when most of the Avestan canon seems to have crystallized). The luridness of Achaemenid royal marriages evidently loomed in Greek imagination; Herodotos heaps scorn on Cambyses for marrying his sisters Atosa and Artystone. And Artaxerxes II would go as far as to even marry his own daughter!

In Zoroastrian tradition, Ahura Mazda inherits many qualities of the Indo-European deity Father Sky, and this was probably strengthened in the Achaemenid era owing to conflation with the Elamite deity Khumban. This is something remarked on by Greek authors; Herodotos says that the Persians "worship the sky, which they refer to as Zeus", where Zeus is often used as the interpretatio graecia of Ahura Mazda in post-Hellenic parallel inscriptions. Moreover, Ahura Mazda is described in one of the Gathas, the earliest Avestan material, as having a daughter in Armaiti ("devotion"), one of the Amesha Spenta, the six most important divinities next to Ahura Mazda.

There's a tradition of associating the Amesha with elements, and Armaiti is associated with the Earth. Thus in some later traditions, Armaiti takes on the role of Mother Earth to Ahura Mazda's Father Sky, and this is sometimes referred to as the first xwedodah in late antique Zoroastrian tradition. However, because cosmogony is only really elaborated on in late, Middle Persian tradition, and because one would expect such an important thing to be remarked on earlier, I don't think the Mazda-Armaiti marriage was necessarily a primeval feature of Zoroastrianism, but rather a reinterpretation of Mazda's generative power in light of the tradition of xwedodah, possibly also influenced by Near Eastern and other more anthropomorphized Indo-European conceptions of the personification of the sky (e.g., Greek Ouranos, Roman Caelus).

So, where does this come from? As I alluded to, xwedodah can also be first-cousin and uncle/aunt-niece/nephew marriage, and for that reason, I suspect this was the original communicated meaning (because it doesn't make much sense to expand it from sibling/parent/child to cousin, nor to consider them to belong to the same category intrinsically). Possibly, it may originally simply referred to intertribal marriage, which the earliest Iranian sources suggest was common (e.g., Zarathushtra is supposed to have married within his Spitama clan). Greek anecdotes as reported in Herodotos say that Cambyses was simply infatuated with one of his sisters and then married the other for good measure (which doesn't make much sense to begin with), but Herodotos' account is very hostile to Cambyses and doesn't appear very accurate (e.g., epigraphic evidence suggests Cambyses was quite conciliatory toward the Egyptian populace and that Herodotos' account contains a fair bit of slander). Generally, any Greek reports prior to the coup of Dareios (who was from a different clan entirely, also slandered Cambyses, and went on to marry Atosa and Artystone himself) are full of dubious material. Xanthos of Lydia, a contemporary of Herodotos, is quoted in Byzantine sources as noting that "the Medes cohabit with their mothers, sisters and daughters".

Herodotos on the other hand suggests the tradition started with Cambyses, sharing an anecdote that the sages of Persia found no law that permitted sibling marriage in general, but did find one that said that the King of the Persians could do whatever he wanted to - but perhaps we should take this more as an anecdotal commentary on Persian legalism from a Greek perspective. It is interesting to note that Egypt, which Cambyses conquered, is indeed one of the other places where close-kin marriage is known to have been practiced in antiquity, and it is possible that he could have married his sisters in a ritual of appeasement, to appear as a legitimate Pharaoh - something we know the Persians tried.

Unfortunately the evidence doesn't point clearly in any one direction, but at minimum, it seems that the Persians had a concept of close-kin marriage into which full-sibling marriage could fit. Interestingly, the last recorded close-kin marriage between Zoroastrians occured sometime in the 14th century; it's mentioned in a medieval rivayat - but at what point it became practiced outside the high nobility is unclear (I recall there being some literary evidence from the Parthian era, which has been argued by de Jong and others to have introduced a different conception of the family's role in the broader social structure). In the high nobility, it's hard to know to what extent such marriage could have been ritualistic or legalistic, to e.g. secure inheritance.

But what we can conclude is that it was certainly neither a universally taboo nor a universally accepted practice, and that even the Greeks' views on it was somewhat arbitrary (half-siblings by the father could marry in at least some Greek city-states, for example).