But you make it out as if that were the way Islam teaches them to behave.
Which is straight up false. Those people are, from the way you describe it, just animals that were played by whoever is behind their actions into doing what they're doing.
Do you know what Islam actually teaches in regards on how to treat the places of worship of other religions?
The first Conquest of Jerusalem by Caliph Umar. The head of the Jerusalem church walks out to greet him and offers Umar to pray in a Jerusalem church (since there were no mosques in the city).
Umar refuses. Why? Because, had he prayed at that church, muslims might have seen it as a holy place and would want to turn it into a mosque. So he refused in order to protect it.
Furthermore, he saw a lack of Jews in Jerusalem. First thing he does is send for Jewish families living in Arabia to come and settle in Jerusalem because the city is holy to them as much as to Christians and Muslims
Using religion as an excuse to commit political actions is not exclusive to any religion. I know, for example, that attacks on Muslims were common place just a few decades past in India. Where those also preached by religious figures in temples? Or were they the actions of small groups who were lead astray?