Humans have chosen to put their faith in science, shunning superstition and anything that could not stand up to scientific scrutiny. Youkai, ghosts and apparitions had no place in the new world.
Gensokyo was also deemed useless to the new world, so priests sealed it away with a permanent barrier. Youkai and the descendants of the brave humans who kept them in check were sealed away in the process as well...
Thanks to their magical culture, youkai could easily breach the barrier around Gensokyo. However, they chose not to do so; in fact, they strengthened the seal in order to prevent more humans from entering.
From the information above I'd say:
The human race developped more and more. Ghosts, vampires or monsters, creatures like Youkai do not belong in such a world. However there is no mention about a god. A god is just like the ghosts and Youkai, still humans have not dropped the ideo of religion, of god.
The border keeps what's in within and the rest out. There are 2 Gensokyos. The one within the border and the visible one, where the abandoned shrine lies.
Youkai can live whereever they please but prefer the "paradise" Gensokyo. I think, many Youkai could heavily influence the world as it is with their powers and at the same time live as a fake human in the human world.
An example is Yukari Yakumo who is said to eat humans outside of Gensokyo. Not-canon is the story about Yukari and Maribel Han (a human who lives in the outer world; she has the ability to see the boundary), who are believed to be the same person.
The fall of the Hakurei border would, in my opinion make travel between Gensokyo and the rest of the world possible for everyone and Gensokyo could be seen as a land just like any other.