From my understanding, Youkai just sort of fade away when humans no longer believe in them (i.e., are fearful of them).
What's up with the resident of the Byakuren temple, then? Shouldn't their relatively peaceful existence be more or less equivalent to brb gensokyo for them? At the very least Murasa and Nue should follow this pattern, even when you could reasonably expect Shou and Nazrin to have different rules (Ichirin is debatable since she originally was a human before turning into a Youkai).