The definition of "religious fundamentalism" can be but is not limited to "the rationale of conservative American Protestants who regard the Bible as free of errors or contradictions and emphasize its literal interpretation, usually without reference to modern scholarship." and "the theological system of any of the churches of western Christendom that separated from the Roman Catholic Church".
However, my answer above would have to be NO! Rather than an INCREASE, there will be the total removal and eradication of ALL "organized religions"....including the Catholic, Protestant, Lutheran, Baptist, Hindu, Buddhist, Muslim, AND believe it or not.... Judaism! And even though the UN does include, at this time, some of these countries or nations that have many adherents to the above religions in it, it will not make it "safe" from the destruction that will occur, since the UN has, in the past, KICKED OUT, countries that did not "buy into" there program or wishes!
Can you imagine what this will mean to the Vatican and its Basilica of Saint Peter, to the religious cathedrals, churches, mosques, temples, synagogues, shrines, and to other religious structures? Can you imagine what is in store for those who officiate in impressive vestments in those religious buildings? Just asking!