How to tell if my fig is ripe
That fig doesn't look ripe to me... but I'm not seeing it in person. Based on the info on the site mentioned below, it's likely the fig is not ripe as the neck is very straight.
Eating unripe figs won't hurt you, though... they just won't taste very good.
Regardless, they should be slightly soft, not firm. According to this site, they will droop on their stems with the weight of their fruit. Here are two of the several photos showing an unripe and very ripe fig:


Fig 1. (above) Not ripe: the fig is too firm and still perpendicular to the stem.



Fig 4. Gravity wins and the fig is ripe and ready, no longer able to support its weight. Note the dewy skin and slight tear in the fruit; it can barely hold its sugary contents at this point.  (Time to grab the snips and go crazy!)

Here's another site with even more info, similar to the previous one. They list three methods to knowing when a fig is ripe: sight, touch, and taste.
Sight:

Go by the color. One of the first signs your figs are becoming ripe is their change in color. Young, immature and unripe figs tend to be small and green in hue. For varieties like Brown Turkey, Chicago Hardy, Celeste, and LSU Purple, the color will change from green to brown or purple as the fruit ripens. In the case of certain fig varieties, like Kadota and LSU Gold, the fruit’s mature color is still greenish — so how do you rely on sight if the fig’s color doesn’t noticeably change? Read on!
Go by the appearance. The fruit itself will droop on the tree as it ripens. This is true for figs regardless of mature color. Young, firm figs tend to stand out perpendicular to the tree. As they ripen and soften, the fruit will bend at the stalk where it is attached to the tree.
Go by the size. As the fruit matures on the tree, it will also grow in size*. The mature size depends on the variety you are growing, but the figs will all increase in size as they begin to mature and ripen on the tree.

Touch:

A ripe fig will be soft to the touch when gently squeezed. Unripe figs are still firm. This is because the ripening process has not yet taken place, and the juices and sugars that are produced as the fruit ripens are not fully present.

Taste:

Ripe figs are delightfully rich and sweet with a soft, smooth texture when they are fresh from the tree. Unripe figs can be rubbery, dry, and lack sweetness. The most effective way to tell your figs are unripe is to eat one before its peak. Most people only eat an unripe fig once before deciding to wait and allow figs to fully ripen before harvesting.