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according to this verse Muslims have no right to impose religion to others. but please note freedom of religion (beliefs) and establishing Islamic state have no conflict with each other. the best example is that many Jews and Christians and even idol worshipers were living freely at the same city of prophet and Muslims and prophet did not impose Islam to them. when an Islamic state is established there are some social laws made for people that all should respect them like laws in the any non-Islamic country but this does not mean all the people leaving in that Islamic state are imposed to accept Islam. they can be non-Muslim and believe in anything they wish but only should respect only to public laws of state. anyway any state has some laws that is lined with basic ideologies of its rulers.

Another note is about duty of establishing an Islamic state. according to Islam when there are the minimum number of serious Muslim supporters required for establishing an Islamic state in a society, so establishing the Islamic state become obligatory for them. and if the mentioned number is less than the min. required it is not obligatory. this law has nothing to do with being majority or minority. but it depends only to determining that if there are enough serious supporters who can form the required power to establish Islamic state or not. Indeed such movements can have political dangers for Muslims living in such a society. so according to Quran if in a society exposing the beliefs can have danger of death for Muslim but has no benefit for Islam so the Muslim has the duty to hide his beliefs from public:

Exactly same as what did messenger of Allah did at first 3 years after recurring his first revelation in Mecca and only secretly invited trusted people to Islam without having any public political movements. but when he found enough supporters he declared his movement against the pagan state of that time publicly that resulted in actions against messenger SAWW and Muslims and they became enforced to live out of city and Meccans were banned to have any relation with them even selling food to them. so some of Muslims died from hunger during those sanctions.

Please note in establishing an Islamic state Islam has problem only with heads of non-Islamic states who resist and fight against inviting their people to Islam and establishing Islamic state. but Islam has no problem with people if they accept or not accept Islam. according to Islam people should be always free in religion. but heads of states are different problem and should be deal with proper methods like the letter messenger of Allah Muhammad SAWW sent to Kings of two main superpower of world at 1400 years ago i.e. Roman empire and Persian empire the only two main power of that time. and finally if they do not accept Islam logically Islam has Jihad for such Kings and dictators who are enemy of God.

In Arabic language the word for State is حکومت which its root is ح ک م and the word حکم in this verse is exactly the root for state and means:"The decision/command/government/judgement is only for Allah." The main function of state is decision making. and any decision in state or government which is not Islamic is rejected in this verse.

According to this verse Muslims have no right to impose religion to others. But please note freedom of religion (beliefs) and establishing Islamic state have no conflict with each other. The best example is that many Jews and Christians and even idol worshipers were living freely at the same city of prophet and Muslims and prophet did not impose Islam to them. When an Islamic state is established there are some social laws made for people that all should respect them like laws in the any non-Islamic country but this does not mean all the people leaving in that Islamic state are imposed to accept Islam. They can be non-Muslim and believe in anything they wish but only should respect only to public laws of state. Anyway any state has some laws that is lined with basic ideologies of its rulers.

Another note is about duty of establishing an Islamic state. according to Islam when there are the minimum number of serious Muslim supporters required for establishing an Islamic state in a society, so establishing the Islamic state become obligatory for them. And if the mentioned number is less than the min. required it is not obligatory. This law has nothing to do with being majority or minority. But it depends only to determining that if there are enough serious supporters who can form the required power to establish Islamic state or not. Indeed such movements can have political dangers for Muslims living in such a society. So according to Quran if in a society exposing the beliefs can have danger of death for Muslim but has no benefit for Islam so the Muslim has the duty to hide his beliefs from public:

Exactly same as what did messenger of Allah did at first 3 years after recurring his first revelation in Mecca and only secretly invited trusted people to Islam without having any public political movements. But when he found enough supporters he declared his movement against the pagan state of that time publicly that resulted in actions against messenger SAWW and Muslims and they became enforced to live out of city and Meccans were banned to have any relation with them even selling food to them. so some of Muslims died from hunger during those sanctions.

Please note in establishing an Islamic state Islam has problem only with heads of non-Islamic states who resist and fight against inviting their people to Islam and establishing Islamic state. But Islam has no problem with people if they accept or not accept Islam. According to Islam people should be always free in religion. But heads of states are different problem and should be deal with proper methods like the letter messenger of Allah Muhammad SAWW sent to Kings of two main superpower of world at 1400 years ago i.e. Roman Empire and Persian Empire the only two main power of that time. And finally if they do not accept Islam logically Islam has Jihad for such Kings and dictators who are enemy of God.

In Arabic language the word for State is حکومت which its root is ح ک م and the word حکم in this verse is exactly the root for state and means: “The decision/command/government/judgement is only for Allah." The main function of state is decision making. And any decision in state or government which is not Islamic is rejected in this verse.

Exactly same as what did messenger of Allah did at first 3 years after recurring his first revelation in Mecca and only secretly invited trusted people to Islam without having any public political movements. but when he found enough supporters he declared his movement against the pagan state of that time publicly that resulted in actions against messenger SAWW and Muslims and there became enforced to live out of city and Meccans were banned to have any relation with them even selling food to them. so some of Muslims died from hunger during those sanctions.

Exactly same as what did messenger of Allah did at first 3 years after recurring his first revelation in Mecca and only secretly invited trusted people to Islam without having any public political movements. but when he found enough supporters he declared his movement against the pagan state of that time publicly that resulted in actions against messenger SAWW and Muslims and they became enforced to live out of city and Meccans were banned to have any relation with them even selling food to them. so some of Muslims died from hunger during those sanctions.

Also movement of Imam Hussain a.s. at Karbala for making Islamic state shows it is highly needed. (Battle of Karbala)

Please note in establishing an Islamic state Islam has problem only with heads of non-Islamic states who resist and fight against inviting their people to Islam and establishing Islamic state. but Islam has no problem with people if they accept or not accept Islam. according to Islam people should be always free in religion. but heads of states are different problem and should be deal with proper methods like the letter messenger of Allah Muhammad SAWW sent to Kings of two main superpower of world at 1400 years ago i.e. Roman empire and Persian empire the only two main power of that time. and finally if they do not accept Islam logically Islam has Jihad for such Kings and dictators who are enemy of God.

Also there is no room for liberal democracy in Islam and based on Quran state is only for God:

قُلْ إِنِّي عَلَىٰ بَيِّنَةٍ مِّن رَّ‌بِّي وَكَذَّبْتُم بِهِ ۚ مَا عِندِي مَا تَسْتَعْجِلُونَ بِهِ ۚ إِنِ الْحُكْمُ إِلَّا لِلَّهِ ۖ يَقُصُّ الْحَقَّ ۖ وَهُوَ خَيْرُ‌ الْفَاصِلِينَ

Say, "Indeed, I am on clear evidence from my Lord, and you have denied it. I do not have that for which you are impatient. The decision is only for Allah. He relates the truth, and He is the best of deciders." http://tanzil.net/#6:57

In Arabic language the word for State is حکومت which its root is ح ک م and the word حکم in this verse is exactly the root for state and means:"The decision/command/government/judgement is only for Allah." The main function of state is decision making. and any decision in state or government which is not Islamic is rejected in this verse.

Please note Islamic democracy is completely different of liberal democracy. Islamic democracy means giving choice to people from options that all of them are previously qualified by Islam. but liberal democracy is giving the choice to people based on no limitation and only based on what their "self" with and want that mostly the with of this "self" is same as with of Satan because Satan has been very active for thousands of years and most of people are deceived by Iblis and Satans.

أَرَ‌أَيْتَ مَنِ اتَّخَذَ إِلَـٰهَهُ هَوَاهُ أَفَأَنتَ تَكُونُ عَلَيْهِ وَكِيلًا

Have you seen the one who takes as his god his own desire? Then would you be responsible for him? http://tanzil.net/#25:43

وَإِن تُطِعْ أَكْثَرَ‌ مَن فِي الْأَرْ‌ضِ يُضِلُّوكَ عَن سَبِيلِ اللَّهِ ۚ إِن يَتَّبِعُونَ إِلَّا الظَّنَّ وَإِنْ هُمْ إِلَّا يَخْرُ‌صُونَ

And if you obey most of those upon the earth, they will mislead you from the way of Allah. They follow not except assumption, and they are not but falsifying. http://tanzil.net/#6:116

وَلَوْ أَنَّنَا نَزَّلْنَا إِلَيْهِمُ الْمَلَائِكَةَ وَكَلَّمَهُمُ الْمَوْتَىٰ وَحَشَرْ‌نَا عَلَيْهِمْ كُلَّ شَيْءٍ قُبُلًا مَّا كَانُوا لِيُؤْمِنُوا إِلَّا أَن يَشَاءَ اللَّهُ وَلَـٰكِنَّ أَكْثَرَ‌هُمْ يَجْهَلُونَ

And even if We had sent down to them the angels [with the message] and the dead spoke to them [of it] and We gathered together every [created] thing in front of them, they would not believe unless Allah should will. But most of them, [of that], are ignorant. http://tanzil.net/#6:111