From a theological rather than a historical standpoint, much of this can be explained. From the beginning of time right up to the present day, God has allowed certain individuals to proclaim many kinds of things, half truths, and even outright lies, and has revealed Himself in doses at various times in human history to various people. But, each time God reveals a little more of Himself, usually we see massive movements in human religious history as a result. That is to say, when a true revelation comes upon mankind, suddenly it changes the face of all human experience with religion from there on out and we can even chart this progress historically across multiple civilizations. After true revelations, there would seem to be very little “reverse” in the zeitgeist of history (after monotheism was introduced, for example) it almost entirely replaced polytheism in the places where it spread the fastest and usually within a couple hundred years of its introduction.
This individual “Abraham” may have unilaterally introduced the idea of true and absolute monotheism to the world (before then every jurisdiction may have had it’s own “god” but usually in a pantheon of some sort), but not even this Abraham possessed the full knowledge of God, and certainly not the Law of God. Later on, Moses introduced a “Law” coming forth from this monotheistic God-concept established by Abraham (which by then many other groups had adopted and called by various names… ‘Aten’ (in Egypt) ‘Chemosh’ (in Moab) ‘Baal’ (in Canaan)…even some forms of Hinduism which are monotheistic, like ‘Jagedishe’…etc. and what some Greek philosophers were able to deduce around the same time as a matter of fact)… Incidentally, after almost everyone else had started to suddenly catch on to this idea of there maybe being “one” God, Moses introduces the Mosaic law, and suddenly other cultures started introducing their own “divine laws” as a result. What is striking about the Mosaic law compared to other divinely-ascribed laws is that most others proceeded by royal decree, but Moses was never regarded as having any royal authority by the OT’s own depiction of him, and that once again flies in the face of what every other culture was doing at the time… even withstanding Gautama Buddha, who taught around the same time as Zoroaster, but taught less of a “religion” than a school of metaphysics that his later followers adapted into a religion.
The uniqueness of the Jewish milieu in the midst of all these world religious events is particularly striking and hard to explain and it’s something no doubt that other cultures would’ve taken notice of, and that’s where individuals like Zoroaster and Mani and even the unknown “Teacher of Righteousness” (talked about in the Dead Sea Scrolls) would’ve tried to step in and produce “innovations” to long-standing ideas prevalent in Judah. One of the things that is striking about the Biblical accounts is what they seem to selectively disregard and what they decide to include. Genesis for instance contains many references to early Israelite and Canaanite mythology that the authors were obviously skeptical about but needed to mention to illustrate greater theological points. Some ancient ideas, even those prevalent among the Israelites, were not included or were only brushed upon as the attempt towards a harmonized simplicity of centralized doctrine was being honed over time, excluding many spurious sources and ideas along the way, one of which may have been that proliferated by Zoroaster and his followers later on, especially during the capture and exile of Judah.
As a result, by the time of Jesus of Nazareth, the area had become a hotbed of religious ideas, proliferated by a number of Jewish sects and various Pharisees and their various disciples, and teachers of all sorts, especially due to the Roman “melting pot” and the expansion of Hellenism. The belief of a Messiah became very popular among the Jews as did many other apocalyptic sects (of which early Christianity was), and the gospel accounts bear witness to this fact in this person of “John the Baptist” preaching before Jesus of Nazareth a similar teaching with apocalyptic undertones. Around this time also we get the rise of the Essenes as well, which were yet another apocalyptic, secluded, esoteric sect that people point to as an inspiration for Christianity (even suggesting that John the Baptist may have been one). In any case, Zoroastrianism has about as much to do with influencing Christianity as the various Judah-isms of the time did, including the Talmudic and Midrash writings and other “updates.”
The reason why Christianity outlasted them all in terms of popularity was because its message was so intricately tailored to the common state of man. If Christianity had been more esoteric (like the Mythras or Gnostics), it would’ve been too secretive to gain widespread appeal. If it had been too common and timely (like those who ran after Bar-Kochba in his revolt), it wouldn’t have maintained any long-term application. If it catered too much to royalty and the upper class in its theology (as some cults did), it wouldn’t have spread among the commoners. If it catered too much to the lower classes, it wouldn’t have gained any esteem with those of privilege and power. If it entangled itself with the intellectual elite around some kind of “knoweldge” or “gnosis”, it wouldn’t have spoken to the daily concerns of uneducated people. If it didn’t have theological insights though, it wouldn’t have inspired its own brand of mystics.
For every reason why Christianity ultimately succeeded despite all that fed into it over time, there’s reasons why all the competing ideologies that fed it didn’t prevail, and if God is guiding history, would He have it any other way?