Are religions mutually exclusive

Yes, they are, and it cannot be otherwise.

Religions answer at least three fundamental questions, how did we get here, what is wrong with the situation, and what is required to rectify the second question. (Though most religions answer the first question, it is of a lesser priority than the following 2.)

Christians say that Jesus was the one true God, taking on a human nature, living a sinless life, and paying on the cross the sin-debt for all who will place 1005 of their hope for reconciliation with God in that act.

Christians say there has only ever been one God, and He has always been God, and always will be.

There are many examples. Any truth claim, by its very existence, deems false any alternative truth claim. Even a claim, "It should be 'both/and,' not 'either/or' " is essentially saying it should be either "both/and" or nothing. It might not be the sort of thing that gives people joy, but it is true nonetheless. This situation regarding truth claims extends to everything, a set within which religion is included.

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"Mutually exclusive" is a very strong term. It implies no overlap whatever. The set of positive non-zero integers and the set of negative non-zero integers are mutually exclusive; there is no integer that is a member of both sets. The question is not "Do some religions hold some beliefs that are not held by all religions?" but "Are religions mutually exclusive?" or, in other Words, "Are all religions completely void of any characteristics/teachings that might also be held by other religions?" Clearly the answer is no.

Regarding religion there are huge areas of overlap among many religions, even if the differences between any two are large enough to define two separate religions. Just name any two or three of the Christian sects, or the sects of Islam, and the point is clear. The different sects do represent different religions, given that religion is a set of practices and not necessarily a clear explication of faith. The Anglican Church and the Roman Church have a lot in common, but differ in a couple of monumental ways, the question of central authority being chief among them. But they are two different religions-- make no mistake about it. There are sects of Judaism as well, and the same idea would apply. Even groups as unlike the standard Christian churches as the Mormons and the Watchtower Bible and Tract Society have a few things in common with the main-line denominations.

To the opposite of the top answer, I believe that all religions are not mutually exclusive. If we represent each religion with a circle of same diameter. Then these circles are neither flying around as the different planets nor completely concentric with one common center. All circles are sharing some common areas. The common area can be small or big among some religions but never zero.

As an example, all religions are calling for same morals in dealing with people: don't kill, don't cheat, don't lie, give charity to the poor, be kind to old people, ... etc. This is an important common area among all religions. Moreover, as another example, compare Christianity with Islam religions. They differ some issues but similar in believing in the same God (the Creator), in believing in the Day of Judgment and second life, in believing in angels, in believing in the holy books of Torah and The Bible (although Christians don't believe in Quran Muslims holy book). So, even in faith beliefs there are common areas in Christianity and Islam. For more information, refer to the related question listed below.