Why did many conquered people accept Islam and what happened to those who did not?

Answer 1

There are two questions here. Correspondingly, the answer will be split in two parts. However, as the second question's answer feeds useful information into the first question's answer, the order of the answers will be reversed.

What happened to those conquered people who did not accept Islam?
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.

Polytheists were forced to convert to Islam with some rare exceptions (such as the Hindus in India). 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).

This system of inequality between Muslims and non-Muslims persisted up to the colonial period, when it reversed. As a result of colonization, the segregated Dhimmi System gave way to a new, modern bureaucratic system where Europeans were the dominant class and natives, regardless of their religion were second-class, unless they became part of the bureaucracy. To do this, a person would require an education in order to become literate and be able to successfully perform functions in the Arab World. As Jews and Christians sought education, they were able to ascend the hierarchy and become relatively powerful compared to the Muslim majority. When the Islamic World became independent, only the Lebanese Christians were able to maintain this dominant position (and only until the Lebanese Civil War of 1975-1991). In other countries, the end of colonization saw a brief rise in Anti-Semitism followed by a mass exodus of Jews from majority-Muslim countries for Israel, UK, France, the United States and Canada. Those Jews and Christians who remained garnered a more equal status than anything that they had previously had under Muslim leadership, but still are unequal in terms of their inability to proselytize, the unofficial "requirement" to avoid offending Islam in public, and the need to seek the authority of high government officials to build new houses of worship or to repair existing ones.

*Although Muslims also had to pay the kharaj in theory, in practice the tax rate for kharaj on Muslims was slight compared to the amount required by the Dhimmi peoples.

Why did many conquered people accept Islam?
It depends on where the conversion took place and the individual converting. Muslims can detail the Islamic claims that Islam is the correct religion and being desirable for society, which I find rather unconvincing. However, there are reasons for conversion to Islam both currently and historically that have much more relevance.

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.

As mentioned before, in most cases, Polytheists were forcibly converted since their religions were not deemed acceptable under Islam.

To Escape Dhimmi Status
If a Dhimmi converted to Islam, all of the legal and social inequalities discussed 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 2

When you are faced by a brutal, murdering, conquering regime, you tend to try and please them. If you did not please them you got killed.