Mango skin is a tough one. It’s edible in the sense that it won’t kill you, but it’s also bitter and tough. Plus, some people are allergic to urushiol, the same compound in poison ivy, which is present in mango skin. So, if your lips tingle after eating mango, skip the peel.
For the rest of us, technically you can eat it. But why would you? The flesh is the star. Save the skin for compost or steep it in tea. Don’t force it.