If boxing can pose serious harm to the one playing, then it’s haram. The Law of No Harm would prohibit it. Now watching it is ok because the one who is watching is not harming himself. Yes, if watching it in a stadium is considered by society as supporting it, then it can become haram.
As for tatbir, some have an issue with it because their claim is that it ruins the image of the Shia, not because it’s haram in itself (since normally tatbir is a type of blood letting and does not cause serious harm).