I think it is very private. The third party app cannot sell the attached email address to others. But I agree if you sign up with the third party using your app

I think it is very private. The third party app cannot sell the attached email address to others. But I agree if you sign up with the third party using your apple id, they will not know you which may end up in creating second account. If they don't have account linking feature, it will be messy.