It is inherent in every religion which claims to be the One True Faith, or the last and final, the highest and ultimate revelation from God, that some portion of its adherents will lay claim to special privileges, or to domination over those not of the same faith.
The logic is inexorable: we are God's elect. We have higher morals, better judgement, the favor of the Almighty. The Others should conduct themselves subordinate to our laws. The Others, if suffered to live among us, should be our servants.
Furthermore, as the teachings of our faith are THE means of salvation for all humanity, we must be free to bring these teachings TO all of humanity, and none must be allowed to get in our way. Other teachings, being false, should not be allowed in the public square.
Taken to its extreme possibilities, this logic could justify simply exterminating those who refuse The Truth, resist the True Faith, those who are so ungrateful as to spurn so precious a gift.
All these strands of thought can be found, at various times and places, in the history of Christianity and Islam. They are less present in Judaism, for two reasons: Judaism is not an evangelical faith, as Christianity and Islam are, and, until the middle of the 20th century, Jews had been without effective political domination of any place on earth for over one thousand years.
Jews do not seek to bring all gentiles into their mode of worship, nor their polity. They are the Chosen People, others are free to worship their own gods, so long as they do not seduce Jews to worship pagan idols. There have been times when Jewish kingdoms have subjugated or slaughtered pagan peoples, but not lately. The conquest and forced conversion of the Idumeans was a disaster, visiting the Idumean, Herod, upon them as the Roman puppet king. There is basis in the Tanach (aka the "Old Testament") to believe that Jews subjected non-Jews to servitude from which Jews were formally exempt, when Jews were politically dominant.
Buddhism, where politically dominant, has its totalitarian strains, just as Christianity and Islam do, even without the core belief in a creator Deity. Hinduism, although not evangelical, is triumphalist, founded on the Aryan conquest of the ancestors of the Dalit. Based strictly on its literature, and traditional culture, Hinduism is the most implacably racist faith on the face of the earth.
To stop short of its totalitarian implications, a religion must either finesse its claims to superiority, OR it must abandon its claim to a uniquely correct approach to salvation.
When multiple religious faiths coexist within the same political entity, there is either a suppressed, low-level conflict, or there is a relaxed attitude that each has its own legitimate path to God. The former contains the seeds of renewed bids for domination. The latter offends the understanding that, e.g., "I am the way, the truth and the life, no-one comes to the Father but through me," or, on the other hand, "There is no God but The God, and Muhammed is his prophet."
The most sophisticated, and well-balanced, answer to any bid for political domination by any religion is, salvation belongs to God, not to the governments of this world. The state, however well-intentioned, is not competent to judge which faith is the true faith. God will act in his own way, as he sees fit, without any need for the assistance of the state.
There is no such thing as a Christian Nation, nor, for that matter, a Muslim Nation. The first Caliphate, like the Holy Roman Empire, besmirched the name of its faith by indulging in decidedly un-Islamic (or un-Christian) pursuits. The Umayyads are particularly blamed for that within the Muslim world, Sunni and well as Shia, but the Abassids committed many of the same sins, and the Arabs ended up in open revolt against the Turkish Sultans, who were in fact the direct successors to the Caliphate.
The most pious rejection of religious freedom is, in a [NAME YOUR PREFERRED FAITH] there will be no conflict between your personal life, your family life, your civic life, your spiritual life, and your political participation. All will be in harmony. (Not mentioned is that rivers of blood would have to be shed to bring that about).
There remain, within every faith in the world, advocates of carnal political dominion, and advocates of either toleration, or outright political equality. Whether the advocates of dominion are a real hazard to others (within as well as without their own faith) depends on how much political room they have to act on their rhetoric, and whether any sizeable number of their co-religionists are actually prepared to take up arms for a doctrine. The potential exists everywhere.
The reason the First Amendment to the Constitution of the United States of America bars Establishment of Religion, is that many in the original 13 states feared efforts to use the machinery of the new federal government to do exactly that. The reason the next clause protects the Free Exercise thereof, is that many feared efforts to infringe individual choice of worship.
That a faith cannot be imposed at the point of a sword, or by means of statute book, police, and prison, says nothing about whether it is, after all the One True Faith, or a true faith, or a complete delusion. Those who really trust in God need not lay their hands on the machinery of the state, to coerce their fellow citizens. God, after all, is omnipotent, and will do what he chooses, in his own good time.