Most non-Christians ridicule young Earth creationism for putting aside science in the name of religion. This is, of course, 100% a strawman, since the creationist claim has never been that science is wrong because the Bible says so Christians might raise this argument to each other. In Christian v Christian debates it's not a disputed premise. But I've never heard one raise the argument against an atheist. but that the atheists are factually wrong about what science says. Obviously they think that science is consistent with the Bible because they think the Bible is true.
Yes, Christianity is a trainwreck of a religion and doesn't even begin to be internally consistent. That's irrelevant to this debate. Because materialism is also a trainwreck of a metaphysics that knocks down the foundation of morality and much more.
The remaining rational argument you can make against young Earth creationism without factually refuting their science is the accusation of motivated reasoning: since they believe an obviously false religion that pulls in a bunch of arbitrary historical claims as dependencies, they have an incentive to dismiss valid scientific evidence that would prove them wrong. And this is a rational point to make (although obviously it doesn't refute their science on its own). Except for one thing.
The materialist scientists are just as religiously motivated!
What do you think a materialist scientist would do if he uncovered seemingly irrefutable evidence that made God a more believable explanation for the universe as we know it than evolution and whatnot? Do you think he'd follow the facts and evidence and believe in the most rational explanation for the data? Or do you think he'd say, "We don't know how to resolve the blaring contradictions with our picture of the universe, but we'll find new evidence eventually if we just keep studying with materialistic assumptions", and sweep the evidence for a creator under the rug? Which does he have a stronger emotional and political incentive to do?
The only person who is capable of neutral science is someone whose creed neither requires any contigent facts to be fulfilled nor precludes any. A Protagonist can do this. Protagonists have no a priori problem with believing in a divine creator, but also no need to satisfy arbitrary historical requirements.
That doesn't mean their science is invalid. None of this is to say either side's factual claims are without any weight, if they can provide credible citations for their claims and explain why their theories fit the data better than the other side's. But it does mean that both sides are equally less trustworthy than a Protagonist scientist. Both sides have the same perverse incentive to see and present evidence selectively.