Why were the conquered people accepting of Islam?

Answer 1

Because they discovered it is the right thing to do.

Mongols tried to invade the whole world, Europe was saved when they stopped their invasion to return to their capital to select a new Khan.

Mongols faced Muslims i the battle of Ain Jalut in palestine where they suffered the first defeat in their history.

Later some of their kings accepted Islam after comming in contact with it and understanding the great values it has.

Answer 2

It was not particularly about the conquered people. People accept Islam because of its message of equaality, truth, justice and human brotherhood. No Muslim army ever conquered Indonesia or Bangladesh, the largest Muslim countries according to populaation.

Answer 3

It is unclear what the question is asking, so see the appropriate sections:

Section 1: Why were conquered peoples accepting of Muslim Rule?
Generally speaking, conquered people accepted Muslim rule because in the Middle Ages, Muslims treated non-Muslims in a way that was superior to contemporaneous civilizations and introduced the concept of religious tolerance (as opposed to Europe which was practicing the exact opposite at the time). However, it is nothing close to equality or Rights. An important thing to note is that the concept of Rights comes out the Enlightenment. Prior to this point, there was a system of privilege wherein the Ruler would provide privileges (out of the kindness of his heart) to a certain group of people to do acts. A person did not have the "right" to anything and this was the mentality worldwide.

The Pact of Omar was a document of submission signed by the Caliph Omar and defeated Christians and Jews during one of Omar's Wars. While the factual accuracy of that story may be doubted, there is no doubt that the Pact of Omar formed the basis for the treatment of non-Muslims in the conquered territories. The Pact of Omar set out a number of regulations that will be described in this answer.

The Dhimmi, or non-Muslim under Muslim occupation was required by the Pact of Omar to pay a number of taxes that were connected with his Dhimmi status. The most famous was the jizya, which was a tax that Dhimmi had to pay for Muslims for the right to not be killed where they stood for not acknowledging Mohammed's Prophecy; it was a form of humiliation. Additional taxes included the kharaj, which was a tax on non-Muslim* land-holdings in the Muslim World. The kharaj was so untenable that most Dhimmi were forced to live in the cities where the tax would not be applicable. There was also inequality concerning the justice system. On paper, a Christian or Jew could testify against a Muslim, but in reality, such testimony was not acceptable and the attempt to defame a Muslim would receive retribution. Christians and Jews were not allowed to build new houses of worship, restore old houses of worship, proselytize in any way (this included religious debate or dialogue), or allow wine or pigs to be shown in public.

Section 2: Why did many conquered peoples convert to Islam?
It depends on where the conversion took place and the individual converting. I leave it to Muslim claimants to detail the Islamic claims to being the correct religion and being desirable for society, so there is no need for me to speak on those claims. However, there are reasons for conversion both currently and historically that likely have a greater weight than Islam's alleged perfection.

Forcible Conversion
As to the claim of forcible conversion even between sects of Islam, there is quite a bit of evidence to show that this did occur. It was never the dominant form of conversion to Islam, but it existed. There are those perpetrated by the Almohads throughout their Empire. 120,000 Muslims were killed in addition to Jews and Christians in the city of Marrakesh alone due to their "incorrect belief". There were also massacres in Safavid Persia against the Jews. There is also Aurangzeb's forcible conversion of Hindus in India and his slaughter of several groups of Hindus who lived outside of his direct authority. There was repression and consistent attacks by the Ottomans of Christian vassals in Europe. Finally, the Ottoman act of Devshirme, ripping Christian boys and girls away from their families to serve the Sultan, is a violation of a person's inalienable right to family.

Additionally, Polytheists were forced to convert to Islam with some rare exceptions (such as the Hindus in India under Akbar the Great). Zoroastrianism was the majority faith in Iran until Islam almost completely extinguished it, both by sword, economic inequality, and brutal repression of Zoroastrian customs (unless they could be Islamicized like Nourouz).

To Escape Dhimmi Status
The Dhimmi, or non-Muslim under Muslim occupation was required by Islamic Law to pay a number of taxes that were connected with his Dhimmi status. The most famous was the jizya, which was a tax that Dhimmi had to pay for Muslims for the right to not be killed where they stood for not acknowledging Mohammed's Prophecy; it was a form of humiliation. Additional taxes included the kharaj, which was a tax on non-Muslim land-holdings in the Muslim World. The kharaj was so untenable that most Dhimmi were forced to live in the cities where the tax would not be applicable. The above answer is also incorrect as concerns justice. On paper, a Christian or Jew could testify against a Muslim, but in reality, such testimony was not acceptable and the attempt to defame a Muslim would receive retribution. Christians and Jews were not allowed to build new houses of worship, restore old houses of worship, proselytize in any way (this included religious debate or dialogue), or allow wine or pigs to be shown in public.

If such a person converted to Islam, all of these inequalities would drop away. Islamic States have historically created a set of benefits that only Muslims could partake, making a choice to be Muslim tied to choices about economic viability (which trades you could work - especially in government) or tied to choices of social standing. These would strongly weight the choice and produce a steady stream of converts by their very nature.

Social Benefits
The majority of Islamic converts in India came from the Untouchable and Sudra Hindu Castes who never would have had a chance to be treated well in Hindu society. However, in Islam all men were equal before God, making conversion an escape from this social suppression. There were similar conversions among slaves in order to find a way to escape from slavery, since it is much more difficult for a Muslim to justify having a Muslim slave than a non-Muslim slave, according to Islamic Law.

Answer 4

During their conquest, the Mongols came in contact with Muslims. Some of them converted, but not all.