My late grandmother had one, of the locally native American variety. They have to be very ripe and soft or they will do the astringent furry mouth thing like a very underripe banana. (squat Fuyu persimmons can be eaten crisp without doing that but I have not managed to because the concept was just too weird in my mouth.) I was always told growing up that they would "pucker you up" if too green (which arguably is true), but my only point of reference as a child was like ...lemons, which is not at all the case.

(Sadly the property was sold off after she died and while my mom and her sisters know the family of the people who bought it, I have no idea whether they kept the tree and I don't know them well enough to go asking for persimmons.)