Why is it that Iran has not had a large Zoroastrian minority (5-10% or more of the total population) until this day the way that Mideastern countries such as Egypt, Syria, Iraq, and certainly Lebanon have had large Christian minorities to this day? Surely, Christians made up every bit as much of the pre-Islamic Middle Eastern population as Zoroastrians did in pre-Islamic Iran, and Christians and Zoroastrians have been equally looked down upon by many Muslims. My guess is because Christianity has had other centres (e.g. Europe) while the only Zoroastrian centre was in Iran?
It might be worth reading these two comments by /u/riskbreaker2987, who is the expert on early Islam here at /r/AskHistorians. Essentially, it seems like we are overstating the popularity of Zoroastrianism. It doesn't help that we basically don't have any Persian sources describing their society at this point, but it does make sense - if Zoroastrianism was not the most dominant religion even in the seventh century, gradual conversion over the centuries is more than enough to explain its further decline even when the faith was not treated particularly badly. Hopefully /u/riskbreaker2987 will be here to further elaborate on this!
Follow-up: Is the fact that Christianity, unlike Zoroastrianism, is an Abrahamic religion also a possible reason for this?
There's a book on the medieval conversion of Iran to Islam, which was more total tha n other parts of the region: Richard Bulliet, Conversion to Islam in the Medieval Period
To follow up on my last sub-question, perhaps the difference with Mideastern Christianity is that the Christians there had spiritual sustenance from Byzantium/Constantinople, as well as Rome and other European Christian centres, while Zoroastrians didn't have a single major centre like that left after the Muslim conquest. Maybe that's also possible?
It's an issue no one is actually certain about. You touched on some of the possibilities, but a few others exist. One possibility is the fact the religions internal theology was shaky at the time; during the Muslim conquests Zurvanism was dominant in the empire, but it's wholly possible that a sizable portion of the population retained pre-Zurvanite beliefs. Unluckily sources are rather limited on this. What is definite is that the modern form is different from the practiced by the Sassanids. So it's possible that the internal disagreements within the Zoroastrian community made them more vulnerable to Muslim missionary activities. Other factors may have included the fact that Zoroastrianism was ingrained in the government and it's likely (It's been a few years since I read up on this; forgive the fact I don't remember my sources off the top of my head) that conversion was expected from those who continued in high ranking government positions. Other things to consider are that Christianity had a long history of existing as a minority faith and that many Christian groups in the region had already faced the pressures of conversion and withstood them in the past.
It's an issue with a decent number of theories, but very little certainty. I'll try and find my old sources and elaborate later.