How did various Islamic polities incentivise conversion?

Question

I have read the Wikipedia article spread of Islam.

The claim is made that conversion at swordpoint was rare

It is now apparent that conversion by force, while not unknown in Muslim countries, was, in fact, rare.

And that non-Muslims had to pay a special tax, the Jizya

They paid a special tax; they were not supposed to wear certain colors; [...]

The wikipedia article about this tax, however, claims that

[it does] not constitute sufficient economic motive for conversion

and that it may have been smaller than another tax (the Zakat), which Muslims had to pay. (further reading suggests that maybe the Jizya had to be paid in addition to, not instead of, the Zakat)

This answer suggests that maybe social exclusion was used

those Dhimmi's have been living separate from Muslims, or were required to wear special clothes, in order to distinguish them from Muslims

but that only works after Muslims are already a majority.

It is my impression that spontaneous mass conversion is historically rare (or even non-existent). For example, places under Roman rule retained their original religions (they did not convert to the Roman religion) until the Christianisation of the Roman empire, which was imposed by force.

So if it wasn't by force, and it wasn't by economic incentives, how did the Islamic Empire incentivise conversion?

Answer 1

The first quote in the question is part of a longer quote from Albert Hourani included in the Wikipedia article on the spread of Islam. That same quote answers the question as follows: "In most cases worldly and spiritual motives for conversion blended together." But what does this mean exactly? As addressed in the question, tax policies probably don't explain much.

The first paragraph of the article mentions that conversion to Islam was:

boosted by missionary activities particularly those of Imams, who easily intermingled with local populace to propagate the religious teachings. These early caliphates, coupled with Muslim economics and trading and the later expansion of the Ottoman Empire, resulted in Islam's spread outwards from Mecca towards both the Atlantic and Pacific Oceans and the creation of the Muslim world. Trading played an important role in the spread of Islam in several parts of the world, notably southeast Asia.

To clarify the second point a bit, a merchant's conversion to Islam could improve their access to trading opportunities. Certain trading ports might allow special privileges to Muslims, and individual Muslim traders might prefer to do businesses with other Muslims.

A few points raised elsewhere in the article:

Conversion to Islam also came about as a result of the breakdown of historically religiously organized societies: with the weakening of many churches, for example, and the favoring of Islam and the migration of substantial Muslim Turkish populations into the areas of Anatolia and the Balkans, the "social and cultural relevance of Islam" were enhanced and a large number of peoples were converted.

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During the following Abbasid period an enfranchisement was experienced by the mawali and... c. 930 a law was enacted that required all bureaucrats of the empire to be Muslims.

It should be clear by now that the precise answer may have varied somewhat according to when and where you are asking about.

Answer 2

Since it was the middle ages, I do not know if these had an important influence, but apart from the purely financial incentive, there might be also:

Apostasy was not really an option. So the proportion of muslim people was likely to increase.

Any faith-mixed wedding would become a muslim wedding. A muslim man could marry a non-muslim woman, but a non-muslim man could not marry a muslim woman, unless he converts to Islam.

There might be similar elements I do not know of. With time, they look like they would motivate a significant number of conversions.