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I seem to remember this discussion coming up a couple of times over the years......though I don't remember there ever being any good answer to it.
If you have a unit, and you are in a religion that considers the shrine's faith as evil, then you can go in enemy lands to burn them.But what if the shrine is in your own realm. Or even your own region? Is there any other way to destroy shrines?
You can defo destroy shrines in your own region, i am just not so sure if its a lords only option or an option for every troop leader, i believe its the later.
I don't recall this being possible. Temples can be closed or raided by the lord, but I don't remember seeing such an option for shrines, which means that if you fail to destroy shrines before taking over a region, you likely will never be able to destroy it as far as I know.