Some people opine that Islamic political system is secular in its nature. By secularism they mean Islam is not to be imposed upon non-Muslim subjects in an Islamic state. Drifted with zeal and eagerness to bring Islam in line with western political systems, they try to oversimplify the points under consideration by presenting some examples from Islamic history and life of our Nabi (ﷺ). Actually such people in declaring Islamic political system as secular one are misled due to the fact that Islam gives certain rights and duties to non-Muslim subjects living in an Islamic state; these rights granted to non-Muslims are relating to their religious, social, economic and political systems. Secularism means non-intervention of religion in political system. In Islamic political system, it is Islam which gives rights and duties to non-Muslim subjects. We cannot say Islamic political system is secular because secularism means non-intervention of religion; but in Islam it is religion which gives rights and duties to non-Muslim subjects.
Secondly what is to be appreciated that non-Muslim subjects in an Islamic state are not given complete freedom to adopt their social, economic and political practices, though they are given complete freedom to exercise their religious practices (e.g. religious prayers; customs; rituals etc). The non-Muslim subjects in an Islamic state are under obligation to forego such social, economic and political practices which are declared as illegal in an Islamic state, unless non-Muslim subjects are exempted from the operation of such laws. For instance, when liquor drinking and ‘riba’ became haram in Islamic state, non-Muslims were also forbidden from those practices. It means non-Muslims are to forego such practices which are declared illegal in Islamic state (unless they are exempted specifically from operation of such law) though such practices are not forbidden in their religion. In other words, in Islamic state, Islam is enforced; enforcement of Islam means non-Islamic systems are eliminated to the extent they are declared as illegal in an Islamic state (for details plz see https://secondriseofislam.blogspot.com/2015/12/enforcement-of-islam-through-muslims.html .
It need not be emphasized that non-Islamic systems would be declared as illegal in an Islamic state only when they happen to be contradictory to Islamic systems; but it does not mean that all non-Islamic systems contradictory to Islamic ones are essentially to be declared as illegal in an Islamic state. For instance, non-Muslims' religious creeds, rituals and customs- though they are contradictory to Islamic ones- are not declared as illegal in an Islamic state. Actually decision in this regard is to be taken in the light of Quran, our Nabi's (s.a.w.w) Sunnah and requirements of the time; requirement of the time is to be made a basis of such decision only if the resultant decision/law is not contradictory to the Quran and if our Nabi's (s.a.w.w) Sunnah happens to be time and people specific in this regard ( for details about time and people specific Sunnah plz see https://secondriseofislam.blogspot.com/2016/05/interpretation-of-deen-and-human_25.html).