One of the issues with pre-modern trade is that international banking and communication as we understand it did not exist, and trust was a major problem across distance and time. This is why dispersed ethno-religious groups could be the vectors by which private trade occurred between civilizations, because there was a circle of trust which existed between these groups despite their particular residence. Jews are the most famous cases of this, but the pre-Islamic Silk Road saw a similar phenomenon with the Sogdians. In the modern world various ethno-religious groups from Gujarat whose traditional occupation is trade also maintain this link to the past of international commerce, which was embedded in kin and religious networks, not transnational corporate institutions. A major way to establish fellow feeling and trust is religion. The Islamic scholar and traveler Ibn Battuta trekked from his native Morocco across the world of Islam, all the way to China. Notably throughout his travels he remained within the confines of a predominantly Muslim subculture. This made sense in regions where Islam was the religion of the majority, or of the minority which was in power (India), but even in China he found refuge among that region's Islamic community (the presence of Muslims was important, because he could always offer up his services as an Islamic legal expert, though in some cases he was obviously drafted into the role). Ibn Battuta flourished in the 14th century, when Islam may have been ceding ground to Western Christendom (e.g., in Spain), but was waxing in the east, and in particular the Indian ocean basin. Already regions of maritime Southeast Asia such as Aceh were Muslim, and within the next three centuries all of what is today Indonesia would come under sway of rulers who were professing Muslims (with the minor exception of Bali). How did this happen? This became the subject of discussion below. There aren't any hard & fast answers here. Much of what I know is from a few books, After Tamerlane: The Rise and Fall of Global Empires, 1400-2000, Power and Plenty: Trade, War, and the World Economy in the Second Millennium, and A Splendid Exchange: How Trade Shaped the World. In none of these books is the Indian ocean trade network the center of the narrative, but all of them focus on its evolution. In particular, with the rise of the Portuguese in the 16th century we get a sense that in that period the Indian ocean was for all practical purposes a Muslim sea! Granted, the peoples who inhabited the shores were not necessarily Muslim, but from the European (and also earlier Chinese) perspective the trade seems to have been captured by peoples who professed Islam. In this lay the possible answer for why maritime Southeast Asia became Muslim, while mainland Southeast Asia did not. The main exception in the latter case are the Chams, a people who happen to be Malay, and so were intimately connected with maritime Southeast Asia.
To me the striking evidence of this happens to be a map of the distribution of schools of Islamic jurisprudence. The details are not relevant, but it is interesting to note that the Hanafi school is found in regions where Turkic or Persian culture was dominant. The Muslims of most of South Asia and China proper are generally assumed to have come from these two cultural stems, and so they are by and large Hanafi, despite the fact that they are neither Persian nor Turkic (the Sunnis of the Balkans are Hanafi as well, whether they're Turkish or not). But look at the distribution of the Shafi'i school. The map does not show it, but the Muslims of Sri Lanka, Kerala, and the Maldives are Shafi'i as well.
It seems then to me that the Indian ocean trade network which was dominated by Muslims between 1000 and 1500 A.D. resulted in the spread of the Shafi'i school of Islam, in particular from the Hadhramaut region of Arabia.
If we didn't know anything else about the history of the Indian ocean except for this map, I think we'd have a sense that the Shafi'i school was spread by people who had some involvement in trade and seaborne traffic. Image credit: Wikimedia