The Tiverton loop was actually "Red", for the larger GWR locos, at limited speed, because of a history of flooding on the main line from the Rivers Culm and the upper Exe - though it could do nothing for Cowley Bridge. Last used as such in the big 1962 floods I think.
The Jct-Town ( the ex B&ER bit ) line was certainly Red, I'm pretty sure the Exe Valley line wasn't though. I did a school project on it, but please don't expect me to remember schoolwork from 35 years ago I have seen a photo of an express at the Jct with a large Prairie preparing to head off to the Town & off to Exeter somewhere.
Culm valley flooding is still an occasional nuisance ( I think, not really local anymore ) but then again flooding where it meets the Exe is a bigger nuisance. Even before all the closures if you wanted to get from Bristol to Torquay when the area was flooded you'd have to go a heck of a way round ( what were the options - Bath-Templecombe-Exeter, Bath-Trowbridge-Westbury-Yeovil which of course is still there, Taunton-reverse-Yeovil via Langport or go through Chard, or via Barnstaple + Plymouth! ).