This is a difficult question, the question of "science or religion?" It is far from a foregone conclusion, and I urge the reader to set aside whatever bias they may have as far as possible, and keep an open mind. Nothing undermines debate so much as the unswerving orthodoxy of the convinced.
By way of introduction, perhaps I should briefly say something about my own experience with this question. As it is with most people who have not grown up in a religious environment, in my early years I was a rather rabid atheist. However, I figured I could strengthen my own case by knowing something of the other side of the argument; as Sun Tzu says:
If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat.
Thus I began my study of the religious literature of the West, with an eye to subjecting it to merciless criticism. Even in my skepticism toward religion, I found that in reading the Bible, Koran, Pentateuch etc. I gained deep insights in to the unconscious motivations of those around me in general, regardless of whether they believed in God. Religion is so deeply embedded in our thinking, even in secular society, that to not understand it is to be wilfully ignorant in a large degree to what makes people tick. This alone is reason enough to familiarize oneself with the basic teachings of world religions, whatever one may think about the truth or untruth contained within them.
Around the same time, I was introduced to a person of extremely wide learning in both the sciences and religion, of whose type I have never encountered before or since. Believing unambiguously in God, he seemed quite able to defend his own peculiar theistic views against any of what I was forced to conclude were my own hopelessly over-simplified objections. In time I began to re-assess my views. The process is still on-going.
I am not religious, but have a deep respect for most religions and the role they play in our world, yet like technology I see religion as having been misused, abused and leaned upon as a crutch for far too long. A hammer can be used to build a house, or to kill. Yet, the hammer is not to be praised or blamed. So like any tool or piece of technology, the question is, of what value is it? Allow me to answer this question, contrasting it where possible with science.
When religion is contrasted with science, all-too-often one is compared with the other in the terms defined by one, to the universal detriment of the other. In other words, a person arguing a pro-science thesis will often evaluate religion according to how well it achieves the agenda set out by science, according to science's methodology, and with the truth-criteria of science in view. This is equally true vice versa.
There is something very, very wrong with this.
When addressing this question, a specific religion needs to be contrasted with the well-defined practice of scientific discovery. The idea that "religion" as such can be defined meaningfully enough to contrast with anything except other vague terms such as "good", "morality", "existence" etc. is the source of a lot of confusion and fruitless debate. As such, the question of "why take religion seriously in the 21st century?" is already too vague, though something may be said through use of an example, which I will offer.
Where "religion" can be taken to have a specific enough meaning, it and science do share something: they both pursue the truth. Allow me to take a particular religion, in this case the Brahmanism of India and apply a philosophical question to it and to science. If one wishes to answer the philosophical question par excellence, namely, "what is real?", then both Brahmanism and science are quite capable of shedding some light on the subject from varying angles. Here is an interpretation of what they both have to say on this, a most important question:
Science: What is real is a confluence of matter and form. The ultimate constituents of reality are at bottom material (I take it that "matter" is understood per se and needs no further definition), but are presented to us in such a way as to take on a certain formal, expressible structure. Example: if you ask what water is, the answer is that on a certain level, it is two hydrogen atoms and one oxygen atom, arranged in such a way that the hydrogen atoms are bonded to the oxygen atom but not to each other. To offer a lower-level account than that, water is composed of a specific arrangement of protons, neutrons and electrons. One can keep going, reducing the account to ever more microscopic levels, but the answer will always ultimately be that water or anything else is a certain formally expressible structure of material elements. So what is real, is ultimately matter and form, which is the sole reality.
Brahmanism: What is real is Brahman. This bears some explanation to Westerners. Atman is most closely translated as "the self", and is an individuated expression of Brahman, which is the ultimate reality, of which Atman is the most easily cognizable constituent or element. Example: if you ask what water is, the answer is that water is the thing that I sense as being wet, which when it falls from the sky is called "rain". The only way in which I can even be cognizant of water in the first place is through my senses. My senses are ultimately an outgrowth of myself, so that when I am experiencing water whether conceptually or physically, I am experiencing myself and myself alone. Extrapolating this point, it must necessarily follow that this is true for all other sensible beings. If so, then this self that is being experienced by all conscious beings is the same thing, if there are other beings at all in this reality. All beings are experiencing the same thing, and that thing is "the self", but universalized. So what is ultimately real is the universal self or Brahman, which is the sole reality.
Two very different approaches to the same question. The answer to the question "why take religion seriously?" is, it depends what you're after.
I have frequently heard that practical reasons need not enter in to the debate when asking why someone would take any particular religion seriously. It is often said that "religion" like any other truth-candidate must stand on its own, and not be simply useful or contingent, if it be in fact truthful. It must be self-evidently true, and not a matter of faith. Shouldn't it?
As has been rightly pointed out by many others, when you get down to one's own ground-floor axioms upon which evaluations are based, science itself requires faith. Now, this faith may well be in "self-evident" principles such as reason and evidence, but ultimately you cannot point to anything that would impel you to accept these principles, apart from the fact that they are useful. Science is only of any value whatsoever to the extent that it serves our highest interests.
True, certain individual religions have made cosmological claims that are wildly out of step with the facts as we take them today, the most widely cited of these claims being the 6000-year cosmology of book of Genesis. There is no denying that this flies in the face of what these days we take to be sufficient evidence to the contrary. However I will shortly call in to question whether, wrong though this 6000-year claim may be, that error is of much relevance to what concerns us most. I would further point out that Brahmanism has a much more accurate estimate in terms of the cosmological time-scale to what modern physics would have us believe, to again be-labour the point that it is much more productive to compare a specific religion with the rather more unambiguous practice of experimental science. Lastly for anyone who judges the committing of fallacies to be in any way revealing about an argument, it is transparently ad hominem to suggest that "you were wrong about X (e.g cosmology), therefore you must be wrong about Y" (e.g ethics).
Then, as I have just alluded to, there is the question of morality. The relative failure of religious doctrine in describing the history of the physical universe has, warranted or otherwise, cast serious doubt upon its authority in this domain as well. However, no one would seriously argue against the idea that all religions have something to say on the matter of morality, and how one can live an ethical life. Religion may or may not be the best means of addressing questions of morality, but not even the most ignorant would deny that it does address them, is at least engaging in an ethical dialogue, irrespective of what one thinks of their conclusions. What of science in this regard?
Science has, as far as this observer can tell, exactly nothing whatsoever to say about morality, at least within the proper sphere of scientific enterprise (which is strictly empirical). You cannot derive an "ought" from an "is", to paraphrase David Hume. In this, science is woefully limited compared to religion, insofar as it puts forth no thesis whatever, and rightly so. Science does not and cannot tell us how we should treat other people, how we should live our lives, or what constitutes the highest good, if it is to remain science. Though it may help to provide supplementary knowledge when the question of morality does occasionally draw from the domain of the physical world, on questions of human valuation, science properly remains mute. To borrow a phrase from Wittgenstein, "whereof one cannot speak, thereof one must remain silent".
So that's it? This question of "science or religion" can never be answered? The two speak a different language and never the twain shall meet?
Practical considerations may rightly be invoked to evaluate this question, and in order to do so, one must evaluate the practical necessity of the domains of knowledge which they respectively inhabit. So, what pressing issues are humanity facing today?
Are we most likely to be destroyed by the daily operations of nature, the palpable, physical pressures which we feel from living in a world of limited means? In other words, is the problem one which science is equipped to address? Or are we most likely to wipe ourselves off the face of the earth due strictly to an inability to live with one another, to die needlessly, hubristically, at the very height of material prosperity? In other words, is the problem one which ethical modes of thinking are equipped to address?
I leave it to the reader to decide.