It is an old saying that a pebble can start an avalanche---keeping with that metaphor, this show had an effort more like a large boulder. A smart, articulate, black hero, who as a bonus was both funny and patriotic. There is great value in puncturing stereotypes, and this show both did that and reduced the fear of the other. In addition to Bill Cosby's Alexander Scott, it provided roles for a large number of black actors (at a time of almost no blacks on television) as both heroes and villains---and even the villains challenged stereotypes.
If Alexander Scott had been merely deadly and tough (which he also was) then it would not have done much to reduced fear of the different. But Scotty was funny, likable, and absolutely trustworthy---someone everyone could be comfortable with. Cosby has gotten a lot of grief---both on I Spy and his later shows-- for not being "black enough" in speech patterns or other ethnic cultural identifiers. Particularly in 1965, being non-racial (which in fact a lot of people are) was a more powerful statement.
As a bonus the show is funny, as well as reasonably smart and nuanced for the genre. It also was willing to show communists as bad guys---something even James Bond films were too cowardly to do.
:-) Let me add to the call from other posts ---- BRING ON SEASON THREE!!!