If drying meat and fish would degrade the cordage, while hung on a wall, under a eave/overhang. Then I feel using cords on traps and left outdoors for more than couple seasons: should disintegrate the cord and deconstruct the trap. But there are lot of old (not centuries old, just decades) fence lines still standing.
Meat is cut into thin slices, fish is generally butterflied, in either case cord doesn't have huge contact area with the protein.
TL:DR; I don't feel cord degradation when drying is warranted.