Some Spaniards hate some Romanians and are hated back by them (I assume so--there are enough Spaniards and Romanians in the world that this must be true). It does not follow that there is hatred between Spain and Romania.
Some scientific claims conflict with some religious claims. It does not follow that there is a conflict between science and religion.
If it did, then by the same token it would follow that there is a conflict between science and science. For there are plenty of scientific claims that are rationally incompatible with each other. Scientists all the time make claims that other scientists deny.
Perhaps this is an unfair way to take the claim of conflict. Maybe the people who claim a conflict between science and religion holds that some well-evidenced claims of science conflict with some religious claims. But suppose some reasonable Spaniards hate some Romanians. That's not enough to count as hatred between Spain and Romania.
What if we take a more symmetric approach? Suppose we say that some well-evidenced claims of science are rationally incompatible with some well-evidenced claims of religion. Is that enough to make for a conflict between science and religion? I think not. But in any case, if by "well-evidenced" we mean ultima facie probable, then it is not clear that this is ever going to happen. For how could p and q be both ultima facie probable and yet rationally incompatible? Surely, the evidence for p would lower the probability of q and the evidence for q would lower the evidence for p to such a degree that p and q would not be ultima facie probable.
Maybe the claim is that there are claims of science that are prima facie probable that are incompatible with prima facie plausible claims of religion. But that kind of tension does not rise to the level of "conflict", or again we have to say science is in conflict with science. For it does happen, not infrequently, that an experiment prima facie shows something that is incompatible with the consequences of a prima facie probable theory. When that happens, the experimental conclusion is denied on grounds of some experimental error or the probable theory is abandoned or the credences of both are lowered. And that sort of thing happens all the time in science and elsewhere. So if this is the sort of conflict that is claimed between science and religion, there is nothing special to it: it is a phenomenon endemic to the intellectual enterprise.
Or perhaps the claim is this: there are claims of science that are scientifically ultima facie justified that conflict with claims of religion that are religiously ultima facie justified. This would make for a conflict between these two systems of justification, I suppose. But it wouldn't be something to worry particularly about. It is easy to generate conflicts between "ultima facie justified" claims when the claims are only ultima facie justified with respect to different subsets of our total evidence. This is even true within science. It is not particularly surprising if there were one conclusion about some phenomenon one would come to if one considered only chemical evidence and another conclusion one would come to if one considered only evidence from particle physics. This sort of "conflict" is not particularly surprising. We need to form beliefs on total evidence, and partial evidence is, well, partial. And in any case unless this kind division in the evidence was wide-spread or concerned really central cases, as opposed to concerning two or three issues, we would not call it a conflict between chemistry and particle physics.
Now, it may be that if the most important Spaniards hated the most important Romanians and were hated back, then that would count as hatred between Spain and Romania (though on the other hand, one might worry about why the elites get to define things). Likewise, if there was rational tension between the most important scientific claims and the most important religious claims, one might say that there conflict between science and religion. But nobody has made out a good case that this is so. Consider two famous cases: (1) evolution and creation, and (2) evolutionary psychology and religious theories of religious and ethical experience. In case (1), the conflict is only there on certain readings of the creation doctrine, and while it is a central religious claim that we were created, it does not seem to be a central religious claim that we were created in the way that the particular creation doctrine claims. In case (2), it is clear that evolutionary psychology is not among the most important scientific claims.
So is there a conflict between religion and science? If there is, it is at most there in a sense that is unimpressive and common in the intellectual life: some claims justified by one body of evidence conflict with claims justified by another body of evidence, and we need to decide what to do on the total evidence. This kind of conflict is present within science whenever theory is in tension with experiment, and a revision is called for.