I think you are missing the point when you say: "Who are you gonna believe -- modern science or a dozens of centuries old document with obvious flaws". Because it is not so much about belief than it is about actions. If a particular person believes that all other people are evil, and wants to commit murder every day, but nonetheless lives a life of helping others and enriching their lives, do you really care what they believe? Does it matter? What if someone believes all kinds of good things, but also happens to run over a small child with their car every day of the week?
For many, Kashrut is not about belief at all, but about having a connection, albeit weak, to thousands of years of history and practice that were in many cases based on belief, and in many cases not. Judaism is one of the few religions in which culture is in many ways stronger than faith or belief--thus the legions of Jewish atheists.