Public access to the bridge is so strategic and integral to the Barmouth-Mawddach Estuary-Dolgellau economy, and beyond, that I can't see anything except structural/safety problems resulting in closure.
I don't believe, despite what it says, Gwynedd Council is genuinely considering actually closing the bridge - it will find the money from somewhere. Indeed, if Network Rail was intending to prevent public access, Gwynedd would no doubt be falling over itself to resist.
The Council is, though, probably trying to generate alternative or other contributory sources of funding for the annual charges by proposing to include Barmouth Bridge in this consultation.
Am not suggesting the petition is wasted effort, though!