Question
Fuyu persimmons are usually eaten firm and not soft while astringent type persimmons must be eaten soft. Ethylene from organic apples or other ripening fruit will soften Fuyu persimmons but this is generally undesirable.
Answer
You only need to dispose of the moldy fruit, then rinse and dry the remaining fruit to remove any mold spores that may have gotten on the surface to reduce the likelihood that more fruit will mold.