Institutional religion and individual religious practice are not the same thing. The two are often so different that one can imagine an individual subscribing to institutional orthodoxy and living one's own religious principles -- and that the two might not have a lot in common.
I sort of promised Nathan Williams (@Vanearl, a total stranger to me) a few thoughts on the subject...as opposed to a much longer essay I could easily write and that would cost me many hours/days/weeks of delay. Technically I did not promise it, but I don't like mentioning I'll do something without actually doing it.
If one admits the statement that institutional and individual religion are not mutually inclusive, pondering its implications should reveal more sensible answers to some vexing questions about the role of religion in politics in particular and society in general.
With any institutional religion -- Judaism, Christianity, Islam -- the organization insinuates into politics. It is inevitable. Thus there is in some form a political movement to each of these institutions. It is particularly true of Islam today, whose deliberate worldwide reach is a modern version of the medieval Roman Catholic Church. It is not an exact parallel; but its aggressive spread and its violent antagonism toward competition bear a striking resemblance to the ancient RCC.
Individual practice is different. It is easy for Jews, Protestants, Catholics, and Muslims to be brethren (or at least to profitably coexist) without an overbearing institutional influence. This does not make a Christian less Christian, or a Muslim less Muslim. To the contrary, it frees the individual to fulfill the obedience and the promise of his practice because true religion is inherently an individual thing.
I do not condemn religious institutions, but I understand their intrinsic flaws. Orthodoxy does not come from the Bible; it comes from an institution that adopts the Bible as the basis of its platform. Orthodoxy is like cement. It dries quickly, sets in place, and doesn't move without enormous consequence. When orthodoxy becomes proscriptive, it is easily corrupted.
Religious institutions do not all suffer the same. Some are more liberal than others. But they are not society's problem with religion. The difficulty is in failure to recognize individual practice as imminently approachable and usually surprisingly tolerant and beneficent.
The non-religious individual who operates from this standpoint will be less likely to alienate religious people, able to easily distinguish the institutional imposition, and be ready to promote harmony without first drawing enemy lines.
There is much more to this. I hope these thoughts will suffice for now.