What if this fabric was bagged up - handled with gloves and a mask - hauled to a laundromat with huge washers -
washed with what? in hot water - and dried - I'd probably want to add all sorts of things - but I've learned that not all chemicals play nicely together. (Bleach and ammonia, for example)
If it got better - yippee!
If it still is icky - then pitch it.
I don't know that much about this mold/mildew/whatever or how sensitive you are to this stuff.
If it only has a few spots, I think I would try to rescue it. If it was really black, I think I would toss it.
But I'm not you and I don't know exactly what your fabrics are looking like.