Why did non-Muslims readily accept Islam?

Answer 1

It depends on where the conversion took place and the particular individual converting.

Accepting the Claims of Islam

There is certainly the Islamic claim to being the correct religion and being desirable for society. Additionally, many non-Muslims heard Islam and were convinced by its morality, its virtues, and its beliefs. This is commonly seen by Muslims as being the dominant form of conversion, but it is difficult to parse out whether or not that claim is historically verifiable.

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 and Sikhs 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 Devşirme, 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 2

Some people easily accept Islam because it appears to have a claim to the truth. Some accept it because they could care less about theological claims, but claiming to believe it enhances their economic or political position. Some accept it to avoid offending those closest to them who may be stronger believers than they are.

There are also numerous people who do not accept Islam or accept it only after a lot of difficulty, so it would not be true that all people easily accept Islam.