..."traditional ideologies and authorities were being torn down there "
They were experimental and short-lived ideologies that were torn down. 20 years earlier it was war era, 30 : depression, 40: hedonism, 50: another war then the industrial revolution and agrarian society.
The nuclear family, single income post-industrial home was an ideal which nobody liked. Feminism cites it a lot, but I think it's only because boomers own the bookshelves, the experiences of their mothers is strong and the boomers came with waves of universities custom built for them. The generation before was lucky to get highschool, meanwhile the boomers were publishing papers, and lots of crappy profs were being brought in with tenure (I know because they were still around in the 90s...)
Communications were revolutionizing our perceptions of race, while war made the roles of gender and the meaning of race more complex. Rodenbery and Lucile Ball both had optimistic visions, which was cool and I think added to the future.
Luceille Ball was smart and powerful and saw a show that fit her ideals. I don't think Trek was at all random and the establishment being overthrown wasn't very established. Trek's influence was minimal, but it predicted the future.... I mean, in terms of multiculturalism and gender. Sulu was on the bridge when the Green Hornet was dealing with Bruce Lee being "too Asian" for a lead role. It's hard to believe how racist people were.
I guess if those are the traditional values you mean, then I agree, they were being slowly eroded. But Trek wasn't wildly successful (at first) and certainly didn't replace a void in the Western psyche. It was given a chance by an idealist, and was successful years later in re-runs.