Climate protests have a specific goal in changing policies and economic practicises.
Burning a Quran has no specific target. It targets muslims as a group entirely. And there is also no goal, no transformation, nothing better to strife for, in it. It is just hate of islam and muslim people. The only target could be to abolish the religion as a whole and ban people from practicising it. that is nothing but persecution. And you cannot argue that the people behind it would want anything less, as they are attacking the key symbol of that religion. Or as a methaphor, you don't slap someone on the wrist by stabbing their heart.