I only once had damage to my persimmon trees by deer. It was when I got persimmon plant in a pot from Edible Lanscaping. There were several fruits on this small tree. Deer tried them all when they were still green. Didn't really eat, just bite.
With all my other persimmon trees I never had any damage even though sometimes fruits are very close to the ground and I have very heave deer pressure here. I do apply Liquid Fence sometimes, not for persimmons but for some flowers that I have close to persimmons. It still could be the reson why deer don't eat my persimmons.
I am in MD, zone 6b. I grow Jiro, Ichi, Hana, Izu, Chocolate, Coffee Cake and Hachiya. The last three are only two year in my yard, so not sure how they will survive long term.
Others are here for many years and I never saw any winter damage on any of them.
To speed up Hachiya or other astringent persimmons persimmon ripe, I put them in a bag with ripe fruits. It can be apples, bananas or ripe persimmons. It really speeds things up. I put just enough persimmons that my family can consume in 2-3 days. When they get ripe, each time I take some out of the bag, I add the same amount of unripe ones.
This way it works for non stop supply of ripe persimmons.
Olga

Deer will eat non-astringent varieties but seem to avoid the astringent ones. In either case it's not a favored food source.

My dad has native to Indiana persimmon trees planted and the fruit tastes amazing! He has not had deer issues. You just have to wait until they’re completely ripe for that great taste! You will quickly learn by taste testing what to look for when ripe (they get a little shriveled). Don’t give up if you try before they are ripe. Keep trying until you get that sweet taste with no astringency. I would stick with native to the United States plants.