Young people don't just think that science and religion conflict, they think that science conflicts with philosophy generally. In fact many of the current pop-sci voices (such as Neil DeGrasse Tyson or Bill the Science Guy) use "philosophy" as a dirty word, and describe it as meaningless and useless. For people like that the idea of a philosophy of science is not a necessary foundation for science, but a contradiction in terms.
This leads to young people saying that things are only true if they are verified by the "scientific method" (which usually remains vague, and when defined never corresponds to what scientists actually do in practice). They often consider the questions along the lines of "why is the scientific method the judge of truth" or "can the scientific method prove that only the scientific method can lead to truth" as meaningless and distractions, rather than as questions that need to be dealt with to justify their beliefs.
But at the same time, most young people are not engaged in science. If they are involved, it is mainly at the lowest undergraduate levels which barely resembles the actual day to day activities of science. Thus they trust only science, while at the same time having only a vague understanding of what science is and does.
We can see this in the article from the OP with statements such as the claim that a Catholic in question would only return to the Church if presented with "replicable, peer reviewed, conclusive proof that a deity exists and I’m guaranteed a happy afterlife.” Why isn't "conclusive" enough proof to get the person to return? Why is it necessary for things to be "replicable" or "peer reviewed." Would they say that Moses should have doubted his many encounters with God, merely because they weren't published in a journal. They are absurd qualifiers in this context, and are only included to sound "science-y".
(That's without getting into the fact that science itself is having a major replicability crisis, and peer review is largely acknowledged to do little to nothing to prevent all but the most obvious fraud or falsehoods from being publish.)
Again, we can see this sort of attitude in this response:
I wasn’t reading anything in particular, but just with school. I always have been very smart, and I was always studious. But as I started to enjoy math and science more, I just realized the discrepancy between religion and science. I guess that was another shaking point. Obviously the two can coexist fairly easily — people do it all the time — but for me, I was one of those more toward the science end of things. Catholicism, especially, did seem to clash fairly well. And then, of course, again, further along the line, that pushed me away from the Church a bit more because of the belief in science that really don’t stack up with religion as far as agreeing with each other.
Note how no specific conflicts are mentioned, and the student also says in passing that the two can coexist because "people do it all the time," i.e. some people believe in both things but its not for him. This isn't phrased in the slightest way as a discussion of a review of the evidence where the evidence for the faith falls short. Instead, it is a matter of personal preference dressed up in scientific terms.
Or again:
Well, I know for evolution there’s that big conflict between the Christian church and science, because parts of the Christian church don’t agree with evolution. But that one I feel like there is a ton of evidence. Evolution, that part, at least, is pretty solid looking to me. But then we learned about the Big Bang theory also in school and, like, that one seemed a little odd to me. I haven’t researched it more in depth, but I don’t know; that one sounds a bit far-fetched to me.
Posters here should generally be aware that there is no conflict between Church dogma and the theory of evolution. However, the student objects that some Christians object to evolution, so there must be some conflict. But it gets worse: the Big Bang is also brought up as a source of conflict, though one in which the respondent supports the Church (i.e. she doesn't think that the Big Bang sounds plausible and so thinks that maybe the Church is right). But the Big Bang theory was created by a Catholic scientist with endorsement of the Pope, and was largely criticized during its creation as a disguised form of creationism! To say that there is no conflict between it and Church dogma isn't going far enough.
My point is that throughout the article when people talk about the conflict between the Church and science they generally aren't aware of what the Church teaches or indeed even what the scientific theories claim. (Incidentally this is consistent with my own experience and what I hear from colleagues in the science faculty). Since they can't even clearly state what the relevant claims are, there is no way that they are empirically tallying up the data for each and saying that one is more likely. Rather, the conflict is more of a conflict between cliques. One is a clique ruled by old guys in black robes who preach at the pulpit, the other is a clique ruled by old guys in white robes who preach at the press conference. But science is trendy now. (Not, of course, actual difficult applications of science, but rather the appearance of science and terms related to it). To use a phrase popular on the internet, young people f***ing love science, but they don't f***ing love the Church.
The good news is that when young people learn the actual history of the Church, or get a grounding in real philosophy, or generally just look into things themselves in an in depth way rather than relying on vague second-hand reports from their teachers and peers they can very easily get excited about all of it, including the teachings of the Church. The bad news is that it is very difficult to get young people to look into things to that level.
It's kind of like posers of any fad: looking like you are in a band is easy and fun; actually learning how to play is hard and unrewarding at the start. Basically the same phenomenon is occurring with science.
