A couple of times now, we've encountered shrines while wandering the countryside; just now I encountered bleakrock shrine on an island somewhere. Even with Religion 9, Xoti couldn't determine anything about it, and the only option we were given was "desecrate the shrine", which I'm sure my religion-strong party would not consider a good idea.

My question: are these just random shrines for atmosphere, or is there some other role that they play in the story??

Depends on the shrine. Some of them contain encounters. Others allow you to rest there for bonuses, if you are able to identify them.

They also don't vanish, so you can return to them and rest again.