Plastics tend to absorb moisture when exposed for certain period of time at a certain temperature. Hence the absorptivity of each plastic differs based on its content, ambient temperature and ambient humidity.
So one need not fear an immediate damage to a spool left open on a rack. The after effects of prolonged exposure to include discoloration and brittleness. This varies from material to material. Similarly absorptivity of moisture too varies.
To prevent this situation, you can always keep the filaments in glass enclosed racks where the environment is controlled. One can also put a back of desiccant which would in turn absorb moisture.