Religious Liberty didn't emerge in the West set-in-stone as we have it today. It evolved. It went back and forth. It was messy. It was dangerous. It was a radical idea for the early 17th century Baptists as Thomas Helwys with his 1613 "Mystery of Iniquity" found out. People who espoused the idea of religious liberty were met with derision, persecution, scorn and death. But that idea evolved from earlier ideas and was a pragmatic approach with a theological discipline. That radical notion took nearly 200 more years to be crystallized in the first phrase or the first sentence of the first amendment, something that were it not for Baptists - particularly John Leland - may never have found a foothold in the Bill of Rights. From there the idea spread and was the basis of most Civil Rights laws in the US. But it was in the West that religious liberty matured over 400 years. It was not just the battle between faith and non-faith, or Christianity verses other faiths; it was the battle within Christianity itself. The West has gone through this fight and settled on religious liberty. The Eastern cultures have yet to do that. Until the Muslim world (and Hindu and all other cultures / governments centered around a faith idea) go through this same 400 year struggle the then-Christian West did, there will be serious strife.
History is a good guide in this regard, and an even better gauge as to the outcome.
Chapter 1 -- How the Idea of Religious Toleration Came to the West by Perez Zagorin