Hooby - Ever since Darwin presented his evidence for evolution by natural selection taxonomists have been trying to work out the exact relationships between species.
The most obvious source of information is physical similarities like analogous structures. Later new fields of research such as biogeography added to the picture. Atavistic and vestigial features provide more useful information. Paleontology has continued to supply an abundance of evidence confirming and refining the picture. Studying the geographic distribution of fossils and their appearance in time provides strong evidence for how modern species evolved. Aquatic mammals are a fantastic example where a whole series of fossils found in Pakistan traces the history of whales back to land mammals.
When it became possible to study DNA it presented a massive source of new knowledge. Either it was going to confirm that the "tree of life" was correct or provide irrefutable proof that that there was no historical relationship between species.
It turns out that even if not a single fossil had ever been discovered genetic evidence proves evolution to be correct. DNA confirmed the relationships between species in most cases and resulted in refinements to the tree in others. There are so many different types of evidence and a few of them are covered in this series. The OP of this thread considers just one of them "Protein functional redundancy".
Please don't think that all scientists do is look for similarities between DNA sequences. That would not be proof of anything. Imagine you are a teacher who suspects your students have been copying from each other in assignments. Just because lots of your students state that the Normal Conquest happened in 1066 is not proof of cheating but there are limitless ways of being wrong about the Battle of Hastings. If 12 of your students all say it happened in 1376 you would have evidence for plagiarism. If you could find dozens of similar common errors you could build up a "family tree" of copying errors. If you studied hundreds of big and small common mistakes you could work out who wrote the original assignment and who copied who, adding new mistakes.
DNA evidence is something like that. The proof is of the same sort that is used to establish paternity and convict violent murderers and rapist.