One of the things many people living in the West ask when they are told about the Muslim vision of a global Sharia governance is why would they care about it, they wrongly assume that Muslims will set their own law and live with it happily, while letting non Muslims carry on with their normal lives as usual, the truth is not as tolerant and nice going as that unfortunately.
Non Muslims will need to follow Sharia just the same as Muslims, they will also need to pay a tribute to the Muslims and declare Islams superiority over them, and what makes this such a confusing thing to westerners is that it seems very technical to them. “So I will pay a little extra tax for the Muslims and live my life, that is not the end of the world, right?” or “OK, I will say that Islam is better and stronger, and will go on with things as usual” will not do, it is not a technical thing at all.
Imagine you are under Sharia, you’re a non Muslim, you are already used to paying 50% of your earnings to the Muslim government, and do that annual ceremony where you kneel and kiss the feet of Muslim clerics, your daughter is married to a Muslim and had converted, better for her – you think.
One day she knocks on your door, her husband had hit her again, only this time he had broken her hand. You remember the last time you went to report this to the police, and the beating you suffered from them, so you will not go this time, she can stay with you until her husband calms down, her baby girl is with her as well.
A few days pass and your son-in-law knocks on your door, he demands your daughter comes back home to clean and cook for him. She leaves and cries, after a few hours he beats her again and she runs away, she does not want to involve you, so she hides in a park, he finds her, and kills her. It’s his right, there is nothing you can do about it, you have seen this happen many times, its come a long way from the “technical” sharia you submitted to.
*Note – honor killings are not in Islam but they are now deeply rooted in Islamic-Arab culture, you will find many Arab courts defending women killers and beaters with the claim that this is very clearly allowed and advised by God.