Deer have chewed off new growth on a few of my trees.  I keep a metal cage around the young trees.

The damage deer could do to your fig planting is highly dependent on available forage and population density. If the local deer populations are high and forage is limiting they will eat just about anything.
If populations are at more sustainable levels and forage is readily available you probably won't see much if any damage.

In general animals don't like to browse figs because of the latex sap produced when they are injured. The sap is an irritant.

The most probable damage to figs committed by deer would be rubbing of antlers on trucks during the fall.

I've also heard ants don't like urine I've tested it it worked for me. I had a colony of them around the base of an in ground tree and I used diluted urine in a spray bottle I didn't see ants around it for weeks so if u have ant problems u can try that

Ok, so I've decided i'll wait for HD or Lowes to get cheap figs in, then plant one as the test - like leaving a goat tied up to see if the lions will come by.