Lack of indoctrination: A large part of how religion functions is by introducing you to religious ideas when you are young and using social pressure (positive for acceptance and negative for rejection) to facilitate belief and adherence. Obviously, this only works in a society that is predominantly one religion. It is incredibly less effective otherwise, due to the social pressure involved being dependent on many people around you expecting you to believe, and holding you with esteem for complying. Without people with those expectations, indoctrination is weaker. The exception is when religion is offered by authority figures, especially at a young age. This can be especially strong, and can carry on even in the absence of that authority figure if they were sufficiently respected.
Being nonreligious due to lack of indoctrination is only a temporary condition if not supported by other "roots". If there is not something else backing it up, it is just nonreligion via ignorance of religious teachings.
Contrarianism: This is a more entertaining influence that acts as an immediate counter to indoctrination by authority or by peers. It is effectively a desire to be a rebel, and oppose both social pressure and authority, which will manifest as a rejection of their lessons by default.
Exposure to multiple religions: Indoctrination is most effective when you are being given an excessive amount of information about one religion in contrast to what you know about others (and the positive spin doesn't help). When, however, you are actually aware of what other religions are, what they believe, and how they affected the societies they existed in, it is suddenly harder to introduce any single religion as obviously superior, and undeniably true. This is far from surefire, however, and may actually be a recipe for someone delving into New Age belief systems, or minority religions that have none of the social pressure that helps to facilitate conversions.
Passionate reprisal: This is what happens when indoctrination does occur, but it is by authority figures that you despise, or cause you to enter a religious social group filled with people you dislike. This leads to distancing yourself from those hated people, by either outright rejecting the relevant religion, religion as an institution, or religion in of itself. This is a very simple form of nonreligion, and if it causes them to adopt actual atheism (rather than just simply refraining from the social interactions that religious institutions entail), a very fragile one.
Reasonable doubt/Critical thinking: The most commonly cited cause for atheism, though far from perfect and rarely the sole influence. Criticizing religious beliefs, and having doubts about them as a result is incredibly helpful in facilitating a nonreligious attitude. The more doubts, and the stronger your critical thinking abilities (and the arguments you are familar with against religious ideology), the more stable you will be in your nonreligious position. The exception is when passionate reprisal is also a factor. When that is the case, the emotional and interpersonal factors that are involved can help to push you in either direction, regardless of the rational strength of either position.
Irreverence: Similar to contrarianism, but not quite. It is a willingness to defy authority and convention. In particular, it is a willingness to disregard traditions and rules that have no rational purpose and to be disrespectful to people or things that do not earn respect. This quality can lead to being nonreligious in of itself. It can also be a product of being nonreligious. But, since it is not as based in stubbornness as contrarianism, a person who becomes nonreligious just because they do not feel the desire to be loyal and respectful by default is not in that position firmly.
Scientific literacy: Basic familiarity with science helps a lot. It not only introduces you to the scientific method, a reliable philosophical process of learning the most that we can about reality under the mild assumption that physical reality actually exists, and the obvious one that we cannot say anything reliable about anything else. In addition, our ever increasing base of scientific knowledge is increasingly coming up with explanations for things that were formerly unexplained, and is even beginning to contradict literal readings of religious texts, to the extent that the incidence of reasonable doubts in even the generally uncritical are increased.
Common sense: This is why one is nonreligious prior to indoctrination and when one is exposed to more than one religion with equal intensity: because we are intuitively nonreligious and nonreligious by default. We are intuitvely aware that there aren't any invisible entities controlling us that we can actually know about, and that it would be nearly impossible to verify the existence of such creatures. But, that is what indoctriation is for: telling us that fairies exist, are serious business, have a laundry list of exploits and demands, and must exist because, if controlling invisible entities didn't exist, there would be no control. And look around you. The world doesn't look like unbridled chaos. Common sense is what makes us hear that and realize that they haven't proved anything, but are just talking in circles. Intuitive logic, as compared to formal logical abilities, are incredibly helpful in fending off the clutch of religious idiocy. (It might not fair so well against claims that are not obviously illogical or pointless, however, and thus is usually only a potential lubricant for reaching other roots, and need not even do that).
[Addendum: the terms here, and the ideas they describe, are by no means exhaustive, and are all, in certainty, speculative bullshit. Just thought it needed mention]