Yes, exposure to religion can bread zealots, and an innumerable number of battles have been fought on the grounds of religion. But religion is not a modern concept and, historically, religion provides social order. The fact that religions largely co-exist in both historic and modern society, shows that it is not an attribute of a religion but rather something in its practitioners. Below I will cover some primary points about the role religion has played, that are both foundational and promotive of a healthy society.
Lets first discuss social order. Niccolo Machiavelli, Thomas Hobbes, John Locke and Thomas Jefferson all discuss that the first founding principle of establishing any society is the collective acceptance of a Sovereign. Whether by force, faith, or solidarity, the people bind together and submit some degree of personal power to the authority, in exchange for safety and communal progress (i.e. we are more capable together than as individuals). Religion is the perfect force to draw in and unify people. It establishes an authority who is omnipotent, yet intangible.
Religion also provides security, strength, purpose and order to society. Marx calls religion the "opiate of the masses" because it can pacify them. If you are in a bad situation, religion tells you to put you're energy into faith, redirecting it from the other common targets like the authority or those who prosper while you suffer.
The concept of an afterlife is a great example of this. Death is a very difficult thing for people to do with. It can often lead to very serious anxiety and unrest in a individual and/or society. None of us know what happens to our souls after we die, this unknown can be a metaphysically devastating realization. Some would become Nihilistic, not concerned of their own actions because after death it doesn't matter. This would also be an issue for society. Placed in a historical context, being unable to comfort the masses causes unrest and leads to the collapse of order. Some religions offer solace and comfort through the concept of an afterlife or rebirth. Order is further maintained though the concept of heaven, which both provides people with the concept that this life is not the most important, and that a good member of society (each society being composed of the members of a specific religion) is promised a life of glory, all thanks to the devotion despite suffering in this life. This therefore promotes social order, helps to establish a reasoning behind religious laws, and comforts the struggling masses (early society was certainly a difficult life style and it was newly emerging, without the advantage of being historically informed).
Though this is more interpretive, I think that evidence of this function of religion is clearly provided from the existence of the Book of Leviticus. The second book of Judaism and Christianity (and following Genesis, because before you can guide people you need to provide them with some answers like, "Where did we come from>"), this contains 613 commandments that touch on all aspects of social life:
1) Public Health - Leviticus contains the laws for keeping Kosher, avoiding shellfish and swine (both can spoil and cause illness if not cleaned correctly). It also contains instructions on how to prepare, clean and preserve meat. The laws go on to even include how to treat illnesses and sets guidelines for quarantine and treat leapers and other diseases that were both common and devastating to a community if not handled correctly.
2) Civil Law - There are a number of very specific civil laws that establish a common set of guidelines that we all abide within a society. Both crime and punishment are laid out. Excessive punishment is also limited within these laws. There are laws about owning land, "no debt shall be held more than 10 years" (including slavery which was a commonly traded commodity in early society).
3) Social Law - In early society, work was a precious commodity, and the community often relied on all its members to provide different portions of what society required to maintain itself. Laws like those surrounding the process of mourning a death (sitting shiva) are set to provide both a structure to loss, but also a limit. In sitting Shiva, after 40 days it is required that mourning ends and that everyone returns to normal life. Another example are The 10 Commandments, such as honor your parents and do not covet your neighbors wife. These may have been the 9 biggest social issues of early society, and the first commandment which compels to you to obey God and his commandments.
Please note that this is primarily Judeo-Christian religious belief. Many "eastern" religions focus on establishing order in "Life" and nature itself, rather than our roles in a society. Other pagan and polytheistic religions focused more on recognizing the limits of humanity compared to the natural forces that immensly powerful (Zeus throws lightning bolts, and Rah is the personification of the Sun). But again, these all provide a rational to fill a void, much of which is still unknown despite human advancement (like the concept of the soul).
Unfortunately, with such a powerful historic influence, it will take a long time (if ever) for it to dissipate from mainstream society. The important thing to bare in mind is that religion or not, people will find justification for divisions and disagreements. Religion itself does not necessitate radicalism, and in most religions order within a society is foundational if not the entire underlying ends.