Not all fruits are climacteric (continue to ripen after picking). With non-climacteric fruits (such as blackberries, raspberries, blueberries, strawberries, watermelons, cherries, grapes, grapefruit, lemons and limes), the general rule is the fresher, the better.
I tried testing climacteric fruits ripened very thoroughly, at the suggestion of raw vegans who seemed to know their fruits, but found that I actually had worse results that way with some and the safest course for me seemed to be to return to mostly minimizing intake of certain fruits like bananas and limit myself to wild berries and small amounts of other fruits. Then I learned from fellow RPD member MuhammadSunshine about prebiotics like resistant starch. I was "resistant"
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to the info he shared at first, but eventually put it to the test and found that my experience has turned out to be the opposite of the standard advice when it comes to starchy fruit, such as bananas and plantains--that I have better blood glucose and less carb intolerance symptoms when I eat more of my fruits/carbs in less-ripened resistant form (I still like my fresh figs thoroughly ripe, though, and just limit my intake
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). I wrote about it in resistant starch threads. Of course, YMMV and I'm not telling you what to do. Also, it hasn't been a cure-all panacea for me. I continue to learn and it's a work in progress for me.
And I actually got some of that annoying chapped lower lip (though no burning) after eating a mango today. It was less ripe than most I've had, so I'll keep your experience in mind, in case it's related (and I'm not certain that it was the mango that caused it). I know I have sometimes seemed to react to the acidity in certain foods and wonder if that could be a factor for me in less-ripe mango, though it wouldn't seem to explain why I handle lemons better than most fruits. It can be puzzling.