As progressive as the show was for its time, it is informed by narratives of the settler imperialism that helped Europeans "conquer the new world".
There's a reason why the intro casts space as "the final frontier." The frontier myth and its accompanying ideology of Manifest Destiny still formed the widely accepted version of U.S. history. Not the land-grabbing, genociding, slavery-spreading version we know today.
Bonus thought: Exploring space was obviously a big thing back then so it's understandable how Roddenberry came up with this line. But when you really think about it, time is the final frontier that we haven't managed to break through yet. Not space.