I recently finished a By Jupiter! run that drastically improved on my previous time, but I unfortunately ran into the bug where the Hagia Sophia conversion event fires multiple times, giving me mass amounts of piety and allowing me to finish the run a few months before I normally would have been able to.

My question is, would this run be allowed (since I had no control over whether the event would fire once or multiple times), or would it be forbidden due to relying on a bug?

Glitches are generally allowed in Speedruns, especially when recreateable. I don't think we are competitive enough to worry about these kind of events, I'd say that's a lucky occurance but potentially something that can be recreated under certain conditions. Similar to amassing large amounts of golds or CBs as a tribal nomad in earlier versions of the game.