Islam came with certain ordinances. like Banning alcohol, prostitution, and stoning to death for adultery.
So there is no separation of state and religion in Islam.
During the early period of Islam, the alcohol was not banned. Before Islam, they were heavy drinkers and it was hard to quit drinking all of the sudden. So Prophet Muhammad (PBUH) gave 20 years of time frame to discourage drinking one at the time.
Even then, not laws were imposed on Muslims because if some people wanted to drink, then they could. Because no coercion is allowed whether in faith, life and general.
Stoning to death for adultery is Arab practice that has been there long before Islam came. And even after Islam came, Islam didn't impose its laws upon the already existing laws which was Arab culture.
To dispute that the stoning to death for adultery is discouraged in the following example; one man came to Prophet Muhammad (PBUH) to repent for committing adultery. Prophet Muhammad (PBUH) pointed that man to GOD meaning repent to GOD in private and move on. But that man was stubborn until he got his wish which was to be stoned to death as the sign of purging himself which was in spirit of the Arab culture despite advised to repent to GOD in private and move on.
The same culture that promoted burying women alive for honor during the time which also the likes of Umar Ibn Al-Khattab (R.A) did bury his daughter alive for honor killing. After accepting Islam, he repent and cried for his mistreatment to his daughter on the tombstone.
Like slavery and drinking, prostitution too was discouraged. But if one woman practiced prostitution, then it would be between her and GOD. You cannot force her not to practice since the coercion is against Islam and so is judgement which rules out imposed ruling that has nothing to do with the laws and orders.
From the birth of Prophet Muhammad (PBUH) to the death of his companionship (R.A), there has never been the laws imposed upon the civilization in regards to faith other than laws and orders. If anything, they focused more the social development like welfare, family benefits, and benefits for disadvantage people.
So-called Shariah laws was coined in 8th century and imposed in 9/10 century which was the purpose of keeping the civilization in control like sheep because the civilization was multiplying thus becoming too challenging. Imposing sharia laws including blasphemy as part of the system was against Islam because Islam is against coercion and the sharia laws is all about imposing and coercion.
One of the biggest challenge was when Umar Ibn Al-Khattab (R.A) was asked to attend to Iraq as leader after the conquest of Iraq. Then, he gave his words for the Christians and Jewish dominated Iraq that no version of Islam or any faith or the matter of ideology would be imposed upon Iraq. In fact, it was declaration confirming that anyone who threatens the spirit of multiculturalism and free to practice expression whether in faith, life and general would be going against Islam, and indeed would be the biggest enemy of GOD.
So that rules out so-called no separation of faith and state. Not to mention 624 years of Sultanate System imposed by its rulers in Ottoman Empire where people from all kinds in terms of ethnicity, faith and background would be allowed to practice the freedom of speech and expression. And those eras were Golden Age of Islam which that concept gifted and lifted Western world from the depression period. During those eras, Ottoman Empire produced bundle of intellectual scientists, thinkers, philosophers, inventors and many more which some of them were heavily engaged in drinking and practiced Sodomite. If they were stoned to death, then the knowledge that we hold on to no longer be there. When western world stopped stoning people to death, only then the knowledge was spread and thus the beginning of the progressive society.
For the end time in Hadiths, Prophet Muhammad (PBUH) warned about Khawarij aka Terrorists that they would try to impose their ideology against the wills of the community regardless of whether the community is Muslim or not, practice Islam in terms of character or not. And they would be from the dog-hell of fire. And the message was clear; kill them by any means necessary for they are anti-peace. And today, Khawarij aka Terrorist-outfits aka ISIS/TTP tries to impose their ideology through bombarding civilians including children and women. TTP alone is responsible for more than 100,000 including children and women in Pakistan just to further its terrorism to promote its ideology which is against Islam in the first place.
Besides, it is common sense why so-called no separation of faith and state is not aligned with Islam because Islam is against coercion in the first place. And anyone who tries to coerce especially in the matter of religion is the biggest enemy of GOD. Let me be perfectly clear; if you try to force Christian, Jewish or Hindu to convert to Islam, then you are the biggest enemy of GOD. You will be right up there along with Khawarij that belong to hell-fire.
No coercion PERIOD. It is no wonder why Arab empire flourished for so long until they imposed Blasphemy Laws in form of Sharia laws which ended their ruling immediately. Then Ottoman Empire flourished with Sultanate System that is in line with the ideology of Separation of faith and state which made inroads for the thriving multiculturalism. And that concept inspired Western world who are now successful following the separation of faith and state.
The moment any nation imposes its ideology upon the nation, and at that moment, that nation can no longer enjoy the favor of GOD. That is what i learned from those patterns. GOD only support the nations, even if it is Christian or Jewish or Hindu that promotes multiculturalism. Because GOD did create all kind of civilizations so we can get to know each other - not to impose on one to another.
Islam is plain clearer truth revealed in clear signs for the people who think and reason doesn't need defenders like you practicing coercion method which gives bad name to Islam and poor impression of A CREATOR, that created us aka mankind with Intelligent and the whole worlds