We wiped out ideologies in Japan and Germany. How? By killing them until they gave them up.
Mesopotamian civilization was destroyed. How? The Mongols killed them and made a pyramid of skills on the banks of the Euphrates.
The Spanish put an end to the Aztec ideology.
It is clearly doable.
I disagree. You can kill a lot of people sure, but there are more to come. And they carry the ideology forward. Sometimes it is in abeyance for a long time, but it does not go away.
By the way, the Mongols who piled up those skulls were Muslims. ISIS is basically following what Tamerlane did in the 1300’s ... using massive violence and force to create a vast caliphate or Islamic empire. That’s 700 years at least that this ideology has been on the rampage. So it’s not that easy to stamp out.
In the meantime, their numbers are growing exponentially and ours are shrinking.