Like Mao Ze Dong said, guerillas move among the peasants like fish swim in the sea. The fewer Muslims there are in the country the less Muslim terrorism there will be.
Consider this: A Muslim man in England decides it is time he made his trip to Mecca, which is religious obligation for all Muslims who can do it. So he arranges his affairs, books his tickets and arrives in Mecca. He marches around the Kaaba 3 times and abuses the Devil. And when he gets back home he is pleased with himself and will have honorific title "Hajji" from then on.
So he will have met the obligations of his religion. Except that he has not. Going on a Haj is only a minor command in the Koran. The big and often repeated commandment is to wage Jihad on unbelievers. But he doesn't do that, nor do 99% of Western Muslims. Why? Because it is obvious that if he does so he is very likely to end up dead or in prison for a long time. He has the normal human instinct for survival.
But in supporting his local Mosque, he supports the teaching of the Mullah. Mullahs are always urging Jihad on their congregants. And there will be some listeners in the Mosque who like the idea of being a hero. They will usually be people who are psychologically or socially marginal but the point is that the Mosque is where they get the sense of mission that they have. If there was no Mosque and no Mullah preaching Jihad, they would go off in some other direction.
So the local Muslim community is the life-support system for Jihadis. Take away that community and no-one would hear of Jihad and would certainly not have it preached at them. So Muslim populations should be sent home not because they have done anything wrong but because they are what in law is called "accessories before the fact". They share a responsibility for the murderous attacks on us committed by their more devout members.
Those who change their religion could stay. How would we know that a conversion was sincere? Easy. Just ask them to say something no Muslim would say -- e.g. "Islam is a false religion and the Koran is the ravings of an insane pedophile"