Their cultures were heavily dyed with Indian culture and religion from trade relations. They even built huge temple complexes so why did they readily accept Islam and how this affect the West and East trade?
To start off,the accounts of conversion to Islam in the local traditions of Malaysia and Indonesia are not considered reliable since they all seem to follow a regular pattern of the ruler getting converted first and the conversion is immediate with miracles, visions and wonders.
The general consensus seems to be that Islam spread in SEA(South East Asia) in three ways:
However the trading element is considered to be the most important. Arabian Islamic traders have been in contact with the region and similar to how Hinduism and Buddhism spread, there was a definite impact. Immigrant Arab communities had begun settling in India and coastal Gujarat ever since the 7th century AD. So Islam was familiar to the Spice trade route of which Malaysia and Indonesia were major hubs. There are indicators of Islamic communities existing in the region, especially major port hubs, as early as 10th and 11th century. However, with the Islamic conquest of Sind, Gujarat and later India, the favor was shifted to Islamic merchants and they started gaining more and more prominence and by extension, influence among the populace and the aristocracy.
The path was then open for the preachers and teachers to travel freely on these merchant vessels to work on spreading the religion. Sufism seems to be the predominant school here. Quoting from the Cambridge History of Islam:
"The scribes and preachers, some of whom had visited Mecca, put the local populations in touch with a wider world community than they had known until then. For even the circle limiting the world of Majapahit, the last great Hindu empire (i 292-15 27), hardly extended beyond the Archipelago, and during the ninth/fifteenth century it steadily crumbled away. Before these holy men from the West the waning glory of the last god-kings of Majapahit paled."
Marco Polo notes that the port city of Perlak was Islamified by the merchants and notes it as the only place where Islam was dominant. But according to the Chinese chronicles, there were ambassadors named Hussayn and Sulayman from the kingdom of Sa-mu-ta-la (Samudra Pasai) who visited the Chinese court in 1282. The first king So while Perlak seems to be the first center of Islam, the faith itself seems to have been more widespread than just the centers.
When Ibn Battuta visits Pasai in 1345, the king was a devout Muslim and notes that the customs he sees as similar to the ones he has seen previously in coastal India. During his time, Pasai is considered to be the end of the Islamic kingdoms in the east. The founding of Malacca in 1400s and its growth into the most prominent port in the Spice trade route played a major role in conversion of the region to Islam. Malacca was founded by Parameswara, which is a Hindu name, but seems to have converted to Islam after marrying a daughter of the king of Pasai and is referred to as Muhammad Iskandar Shah in some sources. Islam continued to flourish and Malacca soon became the Islamic stronghold due to its prominence in the region. It then passed Islam on to its vassals and dependencies such as Pahang,Trengganu, Kedah, Kelantan and Patani. By the 15th century, in the west of the straits, Sumatra, Rokan, Kampar, Siak, and Indragiri had all accepted Islam. And when the Portuguese captured Malacca, in 1511, Islam had already taken a strong root in the region and continued to flourish with Acheh as the new stronghold.
And just to mention, according to the Kedah annals, the last king of Kedah(1136-1179) is said to have converted to Islam and founded the Kedah sultanate. But i cannot find sources to confirm this and the Kedah annals themselves were thought to have been written in the late 18th century, so this claim is probably not true. If anyone has better knowledge on this, please provide the correction.
Sources:
Cambridge History of Islam Vol 2A, The travels of Ibn Battuta - Courtesy of UC Berkeley.