Hunting elephants is legal and can help protection for the species. The real problem is in the context. Is going to an african tax heaven with some questionable people, suffering the second strange accident to the royal family in a short time, and justify the travel later claiming that he wanted to shoot an elephant.

EU project is only partially compatible with monarchy, you either have the power or don't and monarchs can only slowly lose more and more power to bankers with time. Thus, the current anti monarchy trend in many countries of Europe would be expectable. British probably see it coming and jumped of the train.