Allow me to provide the Muslim point of view (or at least one of them). While there may be superficial similarities, I think that they end there. There are some major differences; and perhaps a more logical explanation for the phenomena.

Firstly, simply because one theory is similar to another does not necessarily mean that one actively copied or influenced the other. It is quite possible that, given the evidence, two theories converge on the same explanation; so it is an assumption, simply because there is a similarity in some aspects of the belief, that one influenced the other. For example, the Chinese also believe in the yin-yang duality; does that suggest that Zoroastrianism influenced Chinese thinking? The Mayans also believed in duality; therefore it seems that duality is either (a) inherently built into man's psyche or (b) is so obvious that people can reach the conclusion independently or (c) both. Most world views have a duality built in to them; Zoroastrianism was hardly the first.

Secondly, the Muslim belief is that Muhammad, the person most associated with Islam, was not the originator of the religion. Rather, God, over time, revealed the basic truth of the Universe to many Prophets; which may or may not have included Zoroaster. Unfortunately, these messages got distorted over time; and in the Qur'an, specific examples are given related to the Jews and Christian to this process of distortion of the original scripts. Muslims do believe that Jesus was a prophet, but not the Son of God. It's just that the message got distorted over time. What's unique about Muhammad was that the message has been accurately preserved.

Hence, there is a common source to many religions; one must be careful of the post hoc ergo propter hoc (happened after, therefore happened because of) logical error. Another explanation for similarities between religions is a common source for all of them.

Thirdly, the nature of the belief is inherently different. Yes, there is a duality in Islam. But it's a different type of duality. In Islam, Good or God are superior. God allows Satan to exist for there to be a test for mankind. But God did create Satan. In Zoroastrianism, the duality is much more even-handed.

Also, you can hardly call monotheism a minor difference. It is the distinguishing feature of Islam. Saying that one religion is influenced by another when the key precept is different is stretching it a bit ...

Further, there is no historical indication of an influence on Muhammad. The only one with Zoroastrian knowledge that was close to the Prophet was a man called Salman Al-Farsi (Salman the Persian). He was a Zoroastrian, but rejected it because of the polytheism, became Christian, stayed Christian until he heard about Muhammad, then became Muslim. This was very late in the piece, definitely during the Madinah period, after the basic tenets of the faith had been established.