The social science and medical replication crisis seems like it would be far more impactful than a mathematics crisis, right? Politicians, policy-makers, doctors, etc. all make decisions based on potentially flawed or outright incorrect studies in a way that I don't think is true for the equivalents in math, simply because there aren't decisions and policies up for debate related to much of them (if I am wrong about this, please correct me).
If a flawed mathematical paper were used as the basis for what then became a flawed cryptography algorithm, I can see that having impact if the bad guys noticed the flaw first. But yes, I expect examples like that would be comparatively rare.
In cryptography the math is almost always the strongest part, and it is the side-channel attacks and implementation mistakes that let the bad guys in. When it is the math, the flaw is often that the algorithm has all the desirable properties proved in a number of papers, but has some exploitable structure that analysts can turn into an attack.
I think politicians generally don't make policy decisions based on science. I live in the UK and an obvious example is drug policy. They even fired the scientist whose drug research they didn't like.
But if the science agrees with a decision they've already made then they're happy to use if for justification, even if the science is junk (e.g. the crazy fines on taking children out of school in the UK).
