Kind of like how more experience with nature moved those same societies to not want to destroy it? While it's reasonable to question underlying prejudice and (frankly) very little actual knowledge I do not think that's going to be solved with more experience. We just don't see that reflected in reality. Most of Western society is fossilised, hostile and fundamentally exploitative. Having those attitudes change would involve a complete overhaul of the underlying cultures, which just isn't likely.
So the entire culture doesn't have to be overhauled to have a massive influence. During and after the 60's there was a backlash against the counterculture -- a backlash that was ultimately very effective in some ways, and one which continues today, but I do believe a lot of people will start to once again see that another way is possible once psychedelic use becomes more widespread and mainstream. That potential is one of the few things that gives me a sliver of hope about humanity's future.
There are a significant number of people who view the psychedelic substances they use as teachers, as sacred, as emissaries of gods or other supernatural beings, or as those beings themselves.
Though such views are often dismissed as superstition or magical thinking by many who consider themselves part of "advanced", "civilized" societies, and who view these substances more as neutral tools, such societies' confrontation with these substances is relatively young, and I suspect that as they gain more experience with them their views will change.
Use of these substances have already been the wellspring from which multiple religions have come, and the potential for them to spawn more major religious movements, and with them a much more deferential attitude towards and view of these substances, will only grow as their use increases.