Yes, I developed contact dermatitis from trimming branches off a mango tree. Also had same reaction to crown of thorns. Consequently, both plants no longer reside in my garden.
I can eat mango, but must wear gloves when touching and peeling the fruit.

I know some people can get allergic reactions from the fruit...although nothing too serious.

As for me, I don't have any problems with handling the fruit. I even end up biting the mango peel from time to time (by accident).

Friends of mine went to Mexico on their honeymoon several years ago. While there they ate a ton of mango. Well they both ended up with a light rash. The locals told them it was "mango fever" which happens when you eat a lot of it. I've never heard of that anywhere else and it doesn't really make a lot of sense to me since the oil that causes the rash is in the peel, not inside the fruit.

Too much mango can cause indigestion - the fruit ferments very rapidly in the stomach. The sap of the tree is slightly poisonous and can cause skin rash.