Islam was spread to Southeast Asia (Indonesia, Malaysia, Mindanao, Thailand, etc.) by Arab merchants who started visiting these places during the Umayyad and Abbasid Caliphates. I am talking about the late first millennium and early second millennium.
Indonesia is the largest Muslim country in the world in terms of population, yet counter to what most people would expect, no Muslim army ever set foo in any of these countries to conquer the locals and convert them.
There are also about 30 million Muslims in China, yet again, no Muslim army ever invaded China. The people there converted by contact with Arab traders and missionaries.
In fact, Muslims have a history of NOT converting people after conquest. 3 examples are Spain, India, and Eastern Europe. These regions were ruled by Muslims for several centuries, yet the locals were never forced to convert to Islam.
Since you specifically mentioned S.E.Asia,I think there are more similarities than differences.
Hinduism was the main religion in most of ancient Indonesia,Malaysia,Thailand,Burma,Lao and Cambodia.It was spread mainly by Hindu traders and kings that conquered those countries.Currently,there are no Hindu country in S.E.Asia.Area where Hinduism is still dominant is in the island of Bali.
The declined of Hinduism in S.E.Asia corresponded with the rise of Buddhism.Buddhism was mainly spread by Buddhist monks and lay Buddhist.
Islam was mainly spread by Muslim traders during the 12 and 13 century.
Islam had spread through word of mouth at first and was kept a secret for a long time because pagan Arab leaders held the majority of tribes in control. This meant that the tribe leaders' religion, was basically the religion of everyone in that tribe, whether they liked it or not.
Islam had a very passive period up to a certain point in history until the oppressions caused by the pagan tribes caused the entire believing populace to move to another city.
This began the era of fighting back the oppressors.
For the first time, Muslims were ordered to fight back.
And they fought under the Prophets leadership, against the idol worship ping tribes of Arabia. Everytime they won a war and killed a leader, the people in that tribe were free to chose their religion.
After the Prophets death, many of the people who had accepted Islam, began to switch back to idol worship because they thought the message was over with the death of the messenger.
At this phase, the Caliph chose to fight the tribes who had went back to idol worship.
By the time of the death of the last of the Prophets companions caliph Ali, all of the tribes of Arabia were united under the faith of Islam.
Afterwards, began conquest of other lands through the Umayyad and the Abbasid caliphates. Who were not fully supported by all of the muslims.
Buddhism was a rebellion against the harsh caste society enforced by the Brahmins.
Islam was monotheistic while Hinduism and almost all forms of Buddhism are polytheistic.
You might find "The Genocide of Hindu Women" By Sita Agarwal helpful. It was written by an Indian feminist and discusses history of Hinduism, Buddhism, and Islam and their impact on Indian culture.
http://usminc.org/wymyn.html (you can read it here)
What were the major differences in how Hinduism, Buddhism, and Islam spread throughou
