The reasoning below has been borrowed from pyracantha, where I felt the author had enumerated this topic very well in a non-biased fashion. It has been formatted for ease of understanding.
The topic of converting people of other faiths into Zoroastrianism is a highly divisive topic amongst its followers.
There are two camps that lead this debate within the religion:
The Conservatives (Orthodox), who site the following reasons for NOT allowing conversion in Zoroastrianism:
Philosophical / Religious reasons:
The philosophical reasons claim that to "convert" a person from one religion to another, implies in the first place that the person's current religion is in some way "inferior" to the religion he/she is being "converted" to. Zoroastrianism believes all religions are equally true and no one faith is better or desirable than another. All religions that speak of basically the same principles of righteousness and truth and one God, teach the same values to their followers. All religions that lead to righteous and constructive actions are inspired by God, and will lead their good believers to a heavenly reward. Therefore there is no reason to choose one religion over another. A spiritual searcher should seek within his/her own faith, without trying to adopt other religions. In this view, not only should there be no conversion to Zoroastrianism, but the need should not even arise. Christians should be good Christians, Muslims good Muslims, and Jews good Jews - without coveting the illusory benefits of someone else's faith.
The religious reasons claim that God Himself has placed everyone in his/her faith in a kind of religious destiny, and thus conversion is a disobedience against the God who has given you your specific religion. Many Zoroastrian traditionalists, especially Parsis, believe that the soul, which pre-exists birth into a material body, has chosen, in union with the will of God, to enter a specific religion - just like the soul also chooses its parents in the corporeal world. Just as you can't change your parents once you are born to them, you should not change your religion too. They are both tied to destiny. Attempting to convert is going against the true nature of one's own Soul. For traditionalists, conversion to Zoroastrianism is just short of blasphemy - an act of contempt for the God who has given you birth in a specific tradition. It is true, the traditionalists admit, that many of the great faiths were originally built on conversions from other religions, but these early, founding conversions are justified because they were done under the inspiration of a true Prophet - such as Moses, Jesus, or Mohammed. Once the era of the Prophet is gone, then conversions again become invalid, for only a divine Prophet has the authority to convert people. This leads to the conclusion that hundreds of millions of people are worshiping invalidly, because their ancestors, without the benefit of a Prophet, chose an alien faith - whether willingly or because of coercion. This includes numerous Iranians, who were originally Zoroastrian but were converted to Islam. The conservatives, though they are aware of this, still maintain that even an Iranian Muslim whose Zoroastrian ancestors were forcibly converted to Islam cannot return to the faith of his/her fathers. God, and those individual souls, chose that particular birth, no matter what went on historically. History cannot be reversed. Only a divine Prophet can convert people back to Zoroastrianism. Zoroastrian traditionalists rely on their religious beliefs about a coming Savior - the "saoshyant" - as a final answer to the problem of conversion. When the Savior arrives (a Zoroastrian idea that pre-dated Jewish Messianism and may have inspired the Jewish idea of the Messiah) this divine man will have the authority to convert people. Zoroastrians then hope that all people will be converted to Zoroastrianism through the power of the Savior, who will appear at the End of Time.
Political and Cultural reasons:
The political reasons maintain that when groups of Iranian pilgrims fled an oppressive Muslim regime in Iran in the 10th century AD, they came to Gujarat, a kingdom on the west coast of India. The Kisseh-i-Sanjan (courtesy: www.avesta.org), an epic poem written by a 16th-century Parsi priest, documents the history of his people in India. According to the poem, the pilgrims negotiated with the rulers of Gujarat for safe haven there, and they worked out an agreement. The pilgrims were required to explain the tenets of their religion to the ruler; they were also to learn the local language and speak it rather than Persian. They were also required to adopt the dress of the area rather than wear Iranian garb, they were to celebrate their weddings in the evening rather than in the morning, and they were to put aside their weapons and not wear them at any time. Other traditions say that the Zoroastrian pilgrims were never to convert their Hindu or Muslim neighbors. This promise of non- conversion may not be documented in the poem or other surviving texts, but it is oral tradition, handed down in Zoroastrian culture for a thousand years and more. And the Parsis, as these pilgrims to India were called, have kept their promises. Thus the prohibition against conversion has a longstanding political background
Social reasons:
The social reasons say Zoroastrianism is a strictly ethnic religion. In the traditionalists' historical view, Zarathushtra was not an innovator, but a reformer who practiced the priestly traditions of his ancient Indo-Iranian people. Zoroastrianism, then, does not break traditions, but continues them - reformed from polytheism to monotheism by the divinely inspired Prophet. And these traditions are from time immemorial the exclusive possession of a people known as Aryans. In the West, the term "Aryan" has been permanently discredited by its misuse by the Nazis, and the more neutral "Indo-Iranian" is preferred. For a conservative Zoroastrian, especially those with a more extreme outlook, only those who are Indo-Iranian Zoroastrian, with an unbroken lineage unmixed with any non-Zoroastrian heritage, can be true Zoroastrians. Traditionalists regard Zoroastrianism as more than just a religion. It is an integral culture, which comprises not only faith and practice but an entire lifestyle: language, symbolism, law, clothing, calendar, festivals, food, family life, songs and literature, humor, history, etiquette, gestures, even interior decoration. This integral culture is learned from the earliest moments of life - transmitted from parents to children in an education that no school or sociological study could ever provide. In the traditionalist view, it is impossible to enter into this culture if you have not been born into it - you cannot learn as an adult things you should have learned along with your first steps and words. This culture, and the religion that goes with it, thus cannot be transferred. A non-Zoroastrian married to a Zoroastrian will always be at a loss to understand things his/her spouse takes for granted. And the non-Zoroastrian spouse will bring elements from his/her own culture that are alien to the Z. culture. It is better never to marry outside the culture, as conflict will always follow. The religion is a precious heirloom, which will only be misunderstood and adulterated by outsiders. In this view, intermarriage can only be seen as a threat, which will result in the dilution or even the extinction of the precious culture. And as Zoroastrians, both Iranian and Parsi, migrate away from their native countries, the immigrants are terrified, with good reason, that this heirloom culture will be swept away by the polluted ocean of "Western" culture which surrounds them. Modern culture is a deeply fearsome thing to many traditionalist Zoroastrians.
Emotional and Psychological reasons:
The emotional and psychological reasons stated say that Zoroastrianism, ever since the Muslim conquest of Iran, has been a minority religion. It has been persecuted in Iran for centuries. Even in India, where the Parsis lived more or less undisturbed by their hosts, the Zoroastrians have always remained separate from the majority. The main reason why these minorities have been able to survive through the centuries is because their religion gives them strength. Zoroastrianism has been the coherent core of the people, the rallying point that keeps them going through hard times, poverty, and persecution. Why, then, should it be given away to those who have not earned it, not suffered through the long years of trial? It would mean nothing to an outsider. And so conversion becomes meaningless, or even an insult. .
The Liberals, who site the following reasons for allowing conversion in Zoroastrianism:
Documented History / Doctrinal reasons:
The liberal reformists claim documented history as their strongest argument in favor of conversion. According to the scriptures of Zoroastrianism, which range from the original Gathas of Zarathushtra to doctrinal works written in medieval times, conversion has not only been mentioned but accepted as a practice throughout the long history of the religion There are many passages in the original hymns of Zarathushtra, the Gathas, where the Prophet explicitly claims a mission to convert all people - not just Indo-Iranians. References to conversion occur throughout the Avesta and even in the latest book of the Avesta, written about 200-400 AD, the Vendidad. Scholars both Western and Zoroastrian have written extensively on the spread of Zoroastrianism to Armenia, Central Asia, and as far east as China; other historical texts and archaeological studies prove that Zoroastrianism had spread, through Persian traders, as far west as Asia Minor, Syria, and possibly even Eastern Europe. In lands bordering Iran, many people became Zoroastrians who were not of Indo-Iranian ethnicity. Even after the Islamic conquest, Zoroastrianism was still open to converts, especially servants in Zoroastrian homes who were adopted into the faith by their employers. The strict ban on conversion only dates from the nineteenth century AD.
The traditionalists, faced with Zarathushtra's clear references to converting all people, including non-Indo-Iranians, respond with the counter-argument that it is the TEACHINGS and IDEASof the Prophet that are intended for the whole world, while the RELIGION and its rituals belong only to the Indo-Iranian people. In other words, everyone can be inspired by Zarathushtra's holy words, but only pure-bred Indo-Iranians can practice the actual religion of Zarathushtra. Another variant of this argument is that Zarathushtra's references to a "universal" conversion only refer to a MORAL conversion from wrong-doing to right action, rather than a RELIGIOUS conversion from one faith to another. The more extreme traditionalists discount any conclusions or evidence provided by Western scholarship, regarding all Western interpretations of the Avesta scriptures as misguided, irreligious, and devoid of spiritual insight. Thus the Gathas, when considered as a separate text, are regarded by these traditionalists as a scholarly reconstruction, imposed by Western colonialists. For these extreme traditionalists, the entire Avesta, not just the Gathas, are the words of the Prophet, given by God, and its interpretation must be done in a spiritual and sometimes mystical fashion.
Text of the Gathas:
The liberals maintain that the text of the Gathas, is the only surviving words of the Prophet, and the primary text of the faith. They view Zarathushtra as a great innovator, rather than a reformer of a previous tradition. In the Gathas there is no mention of elaborate mythology, sacred time-schedules, coming Messiahs, Indo-Iranian exclusivity, priestly laws, or strict religious and ritual practices. The tone of the Gathas is philosophical, abstract, and ethical. The rituals, myths, and practices that the traditionalists are so intent on keeping, say the liberals, were DISCONTINUED by Zarathushtra, who never wanted them. It was only later that these religious and social elements were re-introduced into the religion. Therefore, say the reformers, there should be no objection to converting to Zoroastrianism, because the exclusive religious privileges of the Indo-Iranian people were never intended by Zarathushtra.