i've been doing this with my natalina.  it's got a delicate skin that just goes right down with the rest of the fig.  i keep meaning to take pics but i'm too impulsive.  it's hot out there, i got a fig in my hand, and the next thing i know it's in my stomach :).

what varieties do you eat the skin of?

All of them, sometimes i peel but rarely. I hold stem in hand and indulge.
When i eat fig never tasted before i eat very slowly after cutting in half to observe the inside for first time and document with pictures.

Last season my Violet de Bordeaux was a good eating fig and i peeled the skin off and tried eating it seperate.

Try this Mike if you have not it will surprise you in good way with a dark thin skin fig.    ; )

I too Try first separate to eat and then with skin.
If I notice that Skin is bitter,then I eat without skin.
Very rare in very few cultivars the skin is bitter.
On most choice cultivars the skin is very good tasting and is a must to eat the skin.

In most cases, skin and all.

not Kadota/Banana/Peter's Honey

I eat the Celeste skins. 

If the skin of a certain fig was not good to eat, I would just break open the fig and eat the flesh off the inside of the skin.

noss

I've never eaten the skin. Unheard of growing up with the tough, sandpapery skins of the purple figs I grew up with. I still split figs open and just eat the insides. Old habit?
Sue

I eatvthe whole thing unless it's a thick skin and if not fully ripe. How are you suppose to peel a variety like a celeste with very tender skin....? The skin is as sweet as the pulp.

I eat the whole thing!

OMG, no way