There are several distinct issues with Malaysia and this is part of my role in disseminating this information.
Malaysia is a constitutional monarchy based on the British Westminster system. However the constitution of the country enables affirmative action for the majority, which is the ethnic Malays. Minority races such as the Chinese and Indians are granted general freedoms but have much reduced access to government positions, loans, housing subsidies and contracts. Large corporations are required in various ways to have Malays on the Board.
The argument is that upon independence from the British, Malay rights had to be enshrined in the constitution. While Malays are not indigenous they are thought to have arrived several centuries before immigrants from China and India.
Nonetheless, in this day and age the continued lack of meritocracy has led to an increasingly divisive society. Malays generally do not mix widely among Chinese and the Chinese generally do not mix widely with other races. It is a credit to this country that peace is generally maintained and shared interests and colonial influence allows large multinational companies to employ a variety of races and private enterprise has limited discrimination.
But divisions sill exist and the situation does not seem to be relenting. Brain drain is common and most non-Malays that have gone overseas such as myself tend not to return. Those that return have a tough time adjusting.
Where does the Muslim part come in? Malaysia is legally and judicially a secular state. However it is a quasi-religious Islamic country. This is because the majority Malay population is by default Muslim. It is virtually impossible to convert out of the religion and while other races can practice Buddhism, Hinduism and Christianity they are not allowed to preach or convert Malays. If you marry a Malay you must convert to Islam. Additionally, for Muslims, there are separate laws known as Sharia which dictates illegality of homosexuality, drinking alcohol, gambling, eating pork and so on. Sharia is not a guideline, it is a separate legal entity. For example, restaurants serving Muslims during fasting month can be prosecuted.