An example of the limited nature of the independent ideologies of science and religion is the controversy surrounding the birth of our universe. Every written account of the origin of life occludes the obvious truths of all confounding sources.
In the pure science model, we're presented with the Big Bang theory followed by macroevolution. The Big Bang suggests life, in the form of primordial ooze, came from an explosive random creation and sequencing of amino acids. Following this, those simple organisms evolved over time to become the wide array of species existing today, including humankind. The problems with this theory are vast. First, the Big Bang does not explain the inexplicable production of all energy, matter, and life from the pre-existing void. Second, the mathematical probability that the organizing of amino acids took place in the necessary sequences, even over the course of trillions of years, is still trillions to one. Even with the exclusion of all other problematic variables in the scientific explanation of life, one cannot rationally subscribe to this ideology in its pure form. Those who do are by definition, irrational.
The first place people turn to in light of the shortfalls of science is religious philosophy. Though people are often very defensive with their religious beliefs, the underlying truth is that the doctrines of all major religions are very similar. Islamists, Jews, and Christians all share the same God while every other religion offers a similar purpose and moral compass. These similarities may initially seem counterintuitive relative to the conflicts between religions over the ages. However, such parallels can be easily understood when one takes into account the historical and cultural context from which the major religious texts were derived. For example, the original scriptures were written predominantly by men of a patriarchal society, sharing the same desires and fears. This often plays out in the form of guilt, judgment, reward, punishment, and a form of eternity. Where this becomes problematic is in the concept that each of these religions represents the sole path to a rewarding eternity following that judgment.
Under philosophical inspection of this concept, Calvinism's pre-birth assignment of the elect and reprobate is forced to hold true in any religion deemed "the correct religion." This is explainable via the majority of all human life never being exposed to that "correct religion," regardless of which one it is. This immediately counters the concept of a merciful, just, and honorable God, and thus, any judgment made to determine the subsequent eternity of that Person is, by definition, thoroughly invalid. Furthermore, pre-birth determination of eternity represents a philosophical revoking of free will, which contradicts the universal truths religion was founded on.
In consideration of these facts, coupled with the definitions of God, eternity cannot be determined by a single chosen religious path. The implication of this is that no single religion is granted correctness over another. However, as each religion offers a unique perception of theological concepts and historical tradition, it seems apparent that the value of that perception is only realized in a comprehensive, inclusive context. Similarly, the value of such religious paradigms, independent of science, falls under the scrutiny of raw logic and rationality.
In between the theoretical origins via science and religion, is the belief that a non-God life form, such as aliens, is responsible for the genesis of humankind. The dilemma with this theory, however, is as follows: where did the aliens come from, primordial ooze or "the correct religion?" We have already disproved these origins on a rational basis and aliens, being alive, would ultimately have an origin as well. Consequently, any of the existing explanations between pure science and pure religion must still succumb to a creation account of their own.
In conclusion, humankind has been endowed, whether by creation, evolution, or a combination of the two, with the blessing of rationality. And rationally, a conjunction of science and spirituality representing our origin is the only appropriate ideology on which one can arrive.