I have tasted noni, both hard or soft, really bad. Recently I described a noni in my hand as smelling like really rank cheese, and the lady I was talking too said, "I really LOVE smelly cheeses." Sure enough, she ate that noni, and said, "I don't find anything objectionable about it."
Some of the Asimina species in Florida are bad tasting.
The worst fruit that is claimed to be edible, which I have tried several times, is that of the Climbing Ylang-Ylang, Artabotrys odoratissima--- incredibly bitter.
The genus name means "Tree of Bread", and it is included in lists of edible fruits. Maybe after soaking in salt brine for a year, then sun drying, then grinding into a powder....?
PS: The fruit of the true Ylang-Ylang IS edible, when it is fully ripe and wrinkled like a raisin.