Mises on religious (and other) differences:
The pompous statements which people make about things unknowable and beyond the power of the human mind, their cosmologies, world views, religions, mysticisms, metaphysics, and conceptual phantasies differ widely from one another. But the practical essence of their ideologies, i.e., their teachings dealing with the ends to be aimed at in earthly life and with the means for the attainment of these ends, show much uniformity. There are, to be sure, differences and antagonisms both with regard to ends and means. Yet the differences with regard to ends are not irreconcilable; they do not hinder cooperation and amicable arrangements in the sphere of social action. As far as they concern means and ways only, they are of a purely technical character and as such open to examination by rational methods. When in the heat of party conflicts one of the factions declares: “Here we cannot go on in our negotiations with you because we are faced with a question touching upon our world view; on this point we must be adamant and must cling rigidly to our principles whatever may result,” one need only scrutinize matters more carefully to realize that such declarations describe the antagonism as more pointed than it really is. In fact, for all parties committed to pursuit of the people’s welfare and thus approving social cooperation, questions of social organization and the conduct of social action are not problems of ultimate principles and of world views, but ideological issues. They are technical problems with regard to which some arrangement is always possible. No party would wittingly prefer social disintegration, anarchy, and a return to primitive barbarism to a solution which must be bought at the price of the sacrifice of some ideological points.
– Ludwig von Mises, Human Action, p. 180
Insofar as religion is about the individual person or soul, true, they can’t all be right together, but insofar as religion is a social force dealing with life on earth, it’s not a barrier to social cooperation in and of itself.