Persimmons have many virtues. Persimmon trees are lovely, with dark green foliage a plentiful fruit worn like orange Christmas tree ornaments. The fruit is sweet and delicious, and there are only a few small seeds up near the stem. The problem with persimmons is that they only can be eaten when they are absolutely dead ripe. Otherwise the astringent flesh threatens to screw your face into a permanent pucker. A ripe astringent persimmon is not merely soft, it is a bag of jelly. And not just a partial bag of jelly, with some firmness near the stem. A ripe persimmon is 100% squishy.

These persimmons still have some green and won’t be ripe for another month.
Persimmons should not be picked with even a trace of green. There are two types, Fuyu persimmons are a paler orange than Hichiya persimmons. Hachiyas are also more spherical, with a point opposite the stem. Fuyus are more flattened, shaped something like a tomato. The Hichiyas ripen faster, sometimes in a few days after purchase, while Fuyus may take weeks. Fuyus are not as astringent and may retain some firmness when edible.
Years ago, I heard of a method for quickly ripening persimmons. The method is to tightly wrap each fruit in plastic wrap and warm them in an oven for an hour so. The warm oven is obtained by setting the oven to the lowest indicated temperature and then propping the door open several inches. I tried the method at the time and it worked well. Unfortunately, I have forgotten the exact time and temperature, and the Internet seems to be unaware of the technique. So try the method at your own risk, and don’t blame me for any ensuing disaster.

Hachiya persimmons may look blemished and rather beat up, but that’s normal.

Fuyu persimmons are paler and flatter.

There are many other types of persimmon, including several varieties of native American persimmons. some varieties do not have to be super-ripe to lose their astrigency. Persimmons are enjoyed around the world. They are called kuki in many places, and Sharon fruit in Israel.
In the U.S., persimmons are grown mainly in California. I’m not sure why, because the main commercial production in the world is in China and Japan, neither place noted for tropical climate.
Persimmons are harvested well into late fall. This time of year, California farmer’s markets have more than just a few, but elsewhere they are in the supermarkets. Don’t be afraid. Take a chance.