If you use the :SetCoreGuiEnabled() method for the Chat Gui, it doesn’t disable the safe chat bubble. I feel this is a bug because if we’re disabling the Chat Gui, then it’s pretty obvious that we don’t want that either.
IIRC the bubble isn’t actually a CoreGui. I think what needs to happen here is the bubble should be turned into a CoreGui and then it should be connected to SetCoreGuiEnabled.