I think it must be fought with pure power, police, legal, military, public opinion, etc.
If that means revisiting the nature of personal and religious rights and freedoms, let the debates begin.
If the peaceful muslims can't order their religion sufficiently well, to fit into contemporary society, then the state must do so. And if some innocents must be sacrificed for the greater good of mankind, so be it.
The US wisely isolated some Japanese, Italian and Germans during WWII. In fact, there WERE subversives in their numbers.
We should carefully scrutinize Islamic institutions, groups, individuals and err on the side of public safety.
I believe those who would do us harm are NOT entitled to the same basket of rights and protections, for that very reason. The Constitution is NOT a suicide pact.
We are in a state of war with islam, but it is a war of a different type. They see it in very long terms, whereas we (too naively) live for the day and the moment.
We were shelled on the West coast by Japan, along with balloons sent into the Pacific skies. We knew they wanted to sneak into our harbors with submarines, so we put nets across the harbors' mouths.
We feared night attacks, so implemented blackouts, to go with rationing of food, gasoline, rubber and other materials of war.