Science is a self-correcting mechanism. If I try to base my research on a paper that I can't replicate, I'd drop it and base the research on something else. So the reproducibility problem is not lethal.
One usually doesn't try to replicate all the research on which one bases ones paper. Even papers that fail at replication get cited widely.
Science is not particularly reliable.
And yet, we have remarkable technology, and can do medical marvels.
My tentative theory is that there's a lot of knowledge that's less formal than science in engineering, manufacturing, and the practice of medicine which makes it possible to get work done, and some fairly effective methods of filtering information that comes from science.