Okay, I'll try to clear up this confusion.
The Islamic state has the duty of protecting the society from the spread of evil. Non-muslims are free to do what they want so long as they are not harming the society around them. So if a non-muslim chooses to drink alcohol or eat pork, they are entirely free to do so, that is their private issue. Concerning Non-muslims living in an Islamic state:
They are citizens. Their rights, their lives, property, and honor are inviolable. They have the right to employment, education, and commerce. They cannot, however, hold certain government posts that would place them in charge of the religious affairs of the Muslims.
They have the right to practice their religion among themselves as they like without molestation. They have the right to civil courts under their own religious jurisdiction to handle affairs such as marriage, divorce, inheritance, and disputes among themselves.
They must abide by the criminal code of the Muslims. However, they are allowed to engage in those matters deemed lawful in their religion that are unlawful in Islam, like the consumption of pork and alcohol, provided they keep this among themselves and do not make it accessible to the Muslim population. (
SOURCE)
So the general rule is that as long as they are not spreading the behavior that is deemed by Islam to be sinful then they are free to do engage in what they want. There will be no state intervention if they confine their sexual deviation to the privacy of their own homes so that they are not flaunting it in public in any way.
So if they commit an act such as homosexuality publicly, then it is no different from the muslims because they are spreading this licentious behavior in the community.
Shari'ah refers to the entire constitution of Islam, ALL its laws and rulings. So from the Shari'ah are the laws of how non-muslims are to live in the Islamic state and what they can and cannot do. Criminal law is part of Shari'ah and obviously all perpetrators of crimes will be punished, muslim or non-muslim. There is an entire subject of Islamic law devoted to the rulings related to non-muslims living in the Islamic state (
Ahkâm Ahl Adh-Dhimmah). So from this perspective the statement "shari'ah is for muslims only" would be incorrect since many of its rulings deal with how non-muslims are to live in the Islamic state.
However, if by this statement it is meant that non-muslims are not obliged to adhere to Islamic religous practices, then this is undoubtedly true.
As shown in the quotation I provided earlier, this is true. They can have their own courts that deal with civil, marital or other issues specific to their community. But criminal law is an affair that involves the Islamic state.
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