I would also try washing everything first - in hot water - LIKE COLORS TOGETHER - so if in case you had a bleeder, it wouldn't do much noticeable damage.
(Depending on how moldy things were - if it was just 'a touch' - I would give it a try - if the fabrics are the color of charcoal - I would also toss them)
I think I would consider wearing rubber gloves while handling the fabrics, though.
This is another 'it depends' situation -