Speaking for myself, my paramount concern, 100%, for all aspects of the wedding but the ceremony itself and photography was my guests' enjoyment (and they were pretty high on the list for those parts, too!). I can't imagine doing something like this!
The fact that the awful thing was 'customary' or even nice to some of the guests doesn't change my mind that it was inappropriate as a broad or public activity. It's not so much about the content of the prayer (but, oh boy, is it also about the content of the prayer!) as the calling out/the fact that wedding guests knew why the bride was praying with these individual guests.
As for how I would react if I were in this situation? I would walk away quietly but not leave the room. I do not think you need an excuse not to participate (e.g., bathroom) nor do you owe it to someone to tacitly approve by appearing to participate. I don't think you need to make a scene, either.
Side note: Arguing about whether a poster is using a word correctly seems petty, and I hope we can move on from it.