You are right. Majoos means Zoroastrians, and it is used by many Sunni Arabs to describe Persian Iranians (not necessarily all Iranians). I haven’t actually come across a source that confirms the use of “Majoos” against Persians prior to the Safavids era, and the mass conversion into Shia’sim. It could have developed as a result of sectarian hatred that justified the inclusion of racial slurs. I have also noticed that the slur “Majoos” was heavily used by Saddam’s propaganda media to creat a very negative image for Persians during the 8 years war.
Most people that frequently use it, think (rightly or wrongly), that Shia’sim has a been under the influence of Zoroastrians who pretended to have believed in Islam, only to create a different sect that can undermine the religion that ended their imperial glory. The most common justification for this idea is that Shia’sim focuses heavily on strongly hating the first generation of Muslims who have done a great achievements for Islam. The second point in their argument is that Omar is hated more than Muawya, or perhaps more than the devil himself, for no convincing reason other than his role in the fall of Persia.
My two cents.
Shi'ism has nothing to do with Zoroasterianism. Omar is hated by shias, because he is believed to be the one who killed Fatimah, the daughter of the prophet, and also illegally captured the Imam Ali's rights. Also, he is believed to have many bad moral habits.
About Persians hatred for Omar, I think it's better for persians in this thread to explain the reasons.