Holy city of non-state religion does not give line-of-sight benefit

You have to be running the religion as a state religion, in addition to owning the shrine, to get any line of sight benefits. It doesn't matter whether you captured the holy city or founded it though.
 
You don't actually need the shrine to get line-of-sight benefit. But it does need to be your state religion.
 
You need the holy city and be running that religion to get line of sight. If you switch to another religion which you do not own the holy city, or you enact the free religion civic, you lose the line of sight.
The shrine is not a factor here, all it does is spread the religion and give you money.
 
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