You are correct, this is a usage of turn usually reserved to describe political or social changes.
In the first example, the "turn to" social media is being used to abbreviate "recent trends indicating the rise in importance of" social media.
In the second, the "recent turn to" conservationism refers to a rise in the amount of leaders moving toward conservative views.
More generally, "turn to" can be used to describe a social shift that changes the direction of progress, as if the members of the group describes all turned and started walking another direction all at once.
EDIT: @Catija makes a good point, a single person could "turn to" social media to find some pictures of their friends, or "turn to" a library to do research. This is a valid usage, though generally less common.
To my ear, "Turn to" is used to describe finding a solution to a problem. Religious leaders turn to political conservatism because (at least in the US) religious institutions are looking for ways to engage and invigorate the public.
I think this connotation comes from the idea that "turning" implies that this is a new direction. So, someone who rarely uses social media could "turn to" Facebook to reach out to old friends. However if someone is on Facebook most days, I wouldn't describe them as "turning to social media."
EDIT2: @meatie I think this definition fits:
To rebel; to go against something formerly tolerated.
The prisoners turned on the warden.
Webster's online doesn't quite have this usage defined, though this seems close:
to bend or change the course of : divert
a battle that turned the tide of history
While maybe technically incorrect, this usage would be understood by most of the english-speaking world. "Turn," from all of its official definitions, has a definite implication of a change.