The other option is to be willing to sacrifice our own People by being purely reactive - waiting for them to attack is not a smart thing to do, but if we do end up reacting to an attack, we have to be merciless in our response.
Singing kumbaya and sitting on our thumbs only emboldens them. As Golda Meir once said, there can only be peace when they start to love (or mourn) their own children more than they hate us.
Then what exactly do you mean by “exterminate them”.
If you’re talking about the extremists only, how would that be done? Also, even if it were done, there are more extremists waiting in the wings, and more after that. Muslims have one of the highest birthrates in the world. And many of them groom their young to become extremists and terrorists. It’s a high calling.
You will never “exterminate” them because the next wave is always coming of age.
The best option we have is to contain them in their own lands where they can be as extremist as they want among other Muslims. That has been the way of centuries, except when Spain had to push them out of the continent ... but they should never have let them in in the first place. Nor should we or any country that cares about peace and stability.
Let them stay in their own countries and lands. They will then have to deal with their own problems of overpopulation, underdevelopment and resource scarcity.