I will argue here that there is no actual conflict between Science and Christianity. In particular, I will bravely argue that Evolution does not conflict with Creation. This is not to say that the Scientific and Christian communities do not have advocates that argue otherwise.
Automatic mechanisms, repeatable verification, scope of applicability, past and future.
First we need to ask just what is Science? In the modern sense, Science is a methodology for establishing the facts and mechanisms of nature to a reasonable certainty. The facts and mechanisms must be repeatable for verification by multiple researchers. Other kinds of facts and mechanisms are outside the realm of established Science although they may be the subject of current research. The more often a fact or mechanism has been verified and not contradicted, the more established it is.
For example, the fact that a certain blackbird lives in North America can be established by multiple observations by competent observers. A single sighting of a rare bird may be a fact, but has not been established scientifically. Similarly a single experiment verifying the Law of Gravity may be correct, but the law is not established Science until it has been repeatedly verified and not contradicted by other experiments.
An axiom of Science is that nature operates by automatic mechanisms called Laws. Science cannot answer why the Laws behave as they do unless it can be shown that a Law is the completely sufficient consequence of lower-level Laws.
Scientific facts and mechanisms are discovered by observation and logic. We all assume that something seen over and over again is a fact of nature whether it is a thing or a cause-and-effect. Science goes further by deliberately testing with carefully controlled experiments involving reduction and repetition. This is a logical form called Induction. Induction assumes that repeated verification in the present proves a fact or law, and that such aspects of nature do not change with time or location. This is the highest level of proof that we can know and hence the greatest level of certainty that we can achieve. All other methods are much less certain.
Finally, all Scientific facts and mechanisms have a scope of validity. They may be absolutely true but their proved scope is limited to the range of conditions where they have been tested. For example, Newton's Law of Gravity has proved effectively perfect over a wide range of situations, but fails at the huge gravities of black holes and at the subatomic level.
Scientifically established facts and mechanisms can be used to support rational arguments about subjects outside of Science, but the subjects so supported are rational not Scientific. An older meaning of "science" just meant rational. Such logical results are much less reliable than those proved by Induction.
Science assumes that established facts and mechanisms of the present are true in the past. However, note that Science cannot prove past events to the highest level of established, inductive certainty. Science may give us good reasons to believe we know causes and origins in the past but there are problems.
A proposed mechanism in the past leading to facts in the present can be disproved but not proved. We cannot observe a past fact or event, nor can we repeat a past event under controlled conditions, so inductive proof is impossible. Evidence can suggest a cause but does not prove it. Disproof is the only option. If such a proposed mechanism violates established Science or evidence existing in the present, then it is presumed to be disproved. But several such proposals may meet all tests as presently known. Also such proposals are necessarily generalized and gloss over details that might prove critical. As long as there is more than one plausible explanation, there is no way to know which was actually true. Also a better theory may appear that was previously unsuspected. So questions about the past are often never settled.
Mutation, Step by Step, Success Prefers Mutation Over Predecessor
The Neo-Darwinian Evolution proposes that the living species we see today and in fossil evidence developed over time each from the previous by accidental mutation, step by step, guided by the success of each new form in the existing or changing environment. It is assumed that an enormous span of time allowed successes despite the poor likelihood of survivable mutations. This is an extension of Darwin's original Theory of Adaptation where existing variations within a species allow adaptation to changing conditions by the success of those variations under different conditions.
Because any scientific validation of an evolutionary mechanism in the present simultaneously proves the possibility of intentional manipulation, there is no way to decide which actually occurred for all or parts of the living world as we find it. There is no point in arguing which is right, because we cannot know. The Theory of Evolution has proved useful in understanding and organizing biology, but it would work just as well if it were called the "Theory of Intentional Design". This is because a designer would respond to the same environmental pressures as are postulated for Neo-Darwinism.
A problem in discussing Evolution is that scientists and theologians are not engineers or designers. Consequently they do not see evolutionary evidence as a sequence of design choices and refinements, and even quirky explorations of the bizarre or beautiful. It is obvious that evolutionary choices and design choices are difficult, perhaps impossible, to distinguish.
A basic problem in deciding between Neo-Darwinism and Intentional Design is that Science has not established a definite criteria for distinguishing between the accidental and the deliberate. This problem also occurs in archeology, where scientists must decide whether a found stone is a tool or just a rock. We understand that such a distinction should be possible. For example, when we see mountains we assume that they were created by accidental events under the control of natural laws, but when we see Mount Rushmore we instantly know the formation was designed. Some scientists have developed criteria for making such decisions involving recognition of forms with a purpose, but their work is still in progress and not settled science.
Even if we accept the Neo-Darwinism as the fundamental mechanism of the development of species, we know that many existing and past animals and plants were designed by man. Some adapted to environmental conditions imposed by man (wheat and barley). Some were bred by mating types that would not mate in nature. In modern times we have altered DNA to create living things that would not have evolved on their own.
Although we may not be able to prove that any specific living thing evolved from a predecessor, we may find proof that a particular one could not have resulted in accordance with the Neo-Darwinism. If a living thing has a feature that we understand adequately, it may be possible to prove that the feature could not evolve by step-wise change under environmental selection. Some scientists believe that they have shown such "irreducibly complex" features. The more we learn, the more it seems that life itself, the cell, is irreducibly complex.
It may be that both the Theory of Evolution and Intentional Design have both occurred. Theologians will say God's design was first, with or without later evolution or intervention, or that by creating the universe, God set Evolution into motion. Scientists would likely say that living organisms evolved on their own by automatic mechanisms. It may be that an original, intelligent life evolved elsewhere under different conditions that made evolution possible, and planted life here or manipulated a nascent life. If so that would explain existing life on Earth that we proved could not have evolved.
Theologians and lay believers can become confused trying to understand the Bible. The literal truth of the Bible is about God, and its form can be allegorical, poetic, or even a Zen-like stimulus to realization. The Bible is not a science textbook, engineering manual, or gardening guide. Genesis is about God and man, not about the world.
Scientists must assume, as a matter of method, that reality operates by automatic mechanisms. They ignore that man has acted intentionally in the past, and that others, yet to be discovered, may also have done so. Those scientists that vehemently deny all intentionality, have confused method with reality.
Any argument between committed Science and Christian antagonists must be borne stoically. There really is no conflict that can be resolved with current knowledge. Claiming the infallibility of Science or the narrowly literal truth of the Bible are both irrational. There is no need to teach Creation but there is a strong need to add humility to Science education by including the scientific doubt and caution. The excitement of science exploration is not diminished by realizing that the Theory of Neo-Darwinian Evolution needs a lot of work! And is likely not the whole story.