AHC: More Religiously Derived Atheistic Philosophies/Religions

Carvaka/Lokayata and Samkhya were/are atheistic subsets of Hinduism, yes. If I recall correctly, Jawaharlal Nehru identified as a Hindu atheist, but I'm not sure if he subscribed to one of those schools in particular (they're more products of Classical India).

Carvaka is very poorly documented AFAIK.
Atheism is fairly compatible with some intellectual analyses within Hinduism indeed. They are akin to Late Pagan philosophies like Neoplatonism in this regard; the masses are supposed to worship "gods" while the elite knows that there is not strictly speak any such thing as "god" (forgive the brutal oversimplification).
Samkhya is better known and fairly interesting. In my limited understanding, I would class it more as "agnostic" than "atheistic", but the basic point stands.
 
I wrote a senior paper on Zoroastrianism some years ago when I was in college. "Zandik" is a general term for a heretic in Zoroastrianism, and would not necessarily refer to an atheist.

Zurvanism's was probably officially supported in during of the Sassanid era, as there are records of princesses named "Zurvandukht", and Manichaeism was influenced by that more than the so-called "orthodox" sect. (Mani had spent much time in the royal court, and even named one of his books after Shapur I.). Zurvanism certainly wasn't atheist; if anything it added an extra god (that was the "heresy"; that anyone would be above Ahura Mazda).

Mazdakism, another "Zandik" sect is little known because the Sassanids crushed them so thoroughly, though it is believed to have been more of a socialist and anti-clerical. This meant confiscating the wealth of all the temples except for the three main sacred fires Adur Farnbag, Adur Burzen-Mihr, and Adur Gushnasp.

I hope my old paper was accurate, and I hope this helps! :)

I am not very familiar with Preislamic Iranian religions, but AFAIK, this is reasonably accurate. In Islamic times, "Zandaqa" was a vaguely defined (but fairly important) form of heresy that appears to have been broadly similar to Manicheanism; it was dualistic and materialistic, and, IIRC, by no means atheistic at all.
Zurvanism was influential in that milieu, but the problem is that documents are generally a mess about that time and context, so that it not clear how deep Zurvanist influences went.
 
Perhaps have Mahayana Buddhism be more secular so it and its branches are atheistic?

You have one specific branch who is to a point OTL this; Ch'an/Zen. It have monks, yes, but not much clerical, and Theravada-grade (another non Mahayana option pushed beyond maybe) less personal god-theist at least. It sounds kinda non theist to me at times.
 
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