Depends on what the fabric is -- that's a strong disinfecting solution that will likely seriously damage natural fibers. Another disinfecting option is heat (boiling, baking, microwaving), which is safe for some materials and not others. A temp approaching 200F for less than a minute should kill anything interesting.
Again, I don't know anything about crabs so there may be no concerning pathogens at all.
Probably better safe than sorry! What do you think about branches from outside? I feel like I don’t need to be toooooo concerned in the northeast. I definitely wouldn’t be bringing anything in from outside if I lived in Florida!