In this specific context, Jesus was talking to Thomas - though the other apostles had told Thomas that Jesus had returned, Thomas did not believe until Jesus came to him personally. So the verse isn't promoting "blind faith," it's criticizing those who insist on a direct revelation before being willing to accept the truth. I don't think it really applies to science (at least not empirical science), and it is definitely not anti-science.
Extraordinary claims require extraordinary evidence. If a bunch of disciples of a religious figure claimed that he had risen from the dead, is it really the virtuous thing to accept these claims without any evidence?
No indeed, it wouldn't. But there is considerable evidence for the event, some would say overwhelming. There are multiple eyewitness accounts written by different people, sometimes using the same sources, sometimes different ones; disinterested Roman and Jewish historians make mention of it and hostile sceptics of the day mock it as offensive (which of course it is - and still is :)). At no point was this movement stopped in its tracks by the simplest means possible - producing a corpse - and even more incredibly, subsequent claims by followers were conducted in the full glare of publicity, to the point of including famous personalities of the day, even a Roman emperor. If you're going to start a new movement based on a lie, you don't generally include people who have the power to nix your claims in a heartbeat. Not only that but the claims often cost those who were making them their lives. Despite that, it was able to subvert the Roman empire in just a few hundred years.
Archaeology confirms in minute detail that the historical journeys of the early missionaries were as described and one of the authors is called the finest historian who ever lived. Copies of those documents date back to just after the events they described and centuries of banging on them and subjecting them to the closest scrutiny shows that they are as they say they are. Other ancient literature is meager by comparison. We have a handful of copies of Tacitus dated 800 years to a millenium after the events he describes yet no-one sees him as unreliable. Copies of the NT documents number in the thousands, some of which are carbon dated to a few decades after the fall of Jerusalem and all of a sudden they're questionable. Uh huh. Well, we can chuck out most of Roman history and all of Alexander the Great by that yardstick then.
Considering that Thomas had personally seen said religious figure perform miracles and that said religious figure had told Thomas that he would return from the dead in three days, yeah it is.
