I'm no historian by any means but there were no answers and i know a fair bit about the subject because of past interest.

The established monolithic religion of the region was Zoroastrianism and you should think of Mazdakism as an offshoot and sect of Zoroastrianism than its own religion. Manichaeism is nominally an Iranian religion also heavily influenced by Zoroastrianism but has its origins in the Middle-Eastern Gnosticism such as Mandeanism.

Mani's ideas were more radical than Mazdak's (again, think of Mani as Joseph Smith and mormonism and Mazdak as a Protestant) and both of them were seen as heretics by the mobeds of the time.

So, to answer your question, the popular religion of the region (before the muslim conquests) was Zoroastrianism and manichaeism, mazdakism, mazdaism and other offshoots/sects never really had a big following in the region (Manichaeism did however enjoy some popularity outside of persia). In the arabian peninsula, pagan beliefs were popular.

As the first monotheistic religion, Zoroastrianism (along with vedism to some degree) influenced a lot of religions and it's thought to be the origin of the abrahamic faiths.