Opposing AI has become the faith leader. 

Previous saves are not locked out of finishing / rushing a holy site. Holy site vanished from build list. F'all I can do now right? 

Maybe build wonders get back in charge?

Also apparently I can still pick the Tenants in later turn. Working as intended?
I think something prompts a rewrite in the autosaves? All saves? Religion tags?

auto-save 1537.ctr

auto-save 1532.ctr

Babylonians Turn 43 unclear faith systems at work.ctr

Babylonians Turn 44 religion flipped .ctr

The way to replicate this bug is to have a little faith. 

Tenants I chose were influence T1 influence T2 and give alms T3

Civics I had were +5 inf on capital / and / religious hostility.

Expected behavior. Some kind of polite "hahaha get yoinked it" pop up at least.
If I had to expect the bug was created when the AI algorithm decided to flip - and when they did - their holy site did not remain true to their old religion. It became a holy site for my religion. Potentially this is a build order thing - it was in their queue. They flipped to my religion. Rushed it. And built my religions 1st holy site. I think mine was in my queue as well but I'm not 100% sure.