As an addendum to The Incompatibility of Islam and the West, let me add that the case against Muslim immigration is political not religious. It is because Muslims are politically subversive that their immigration must be curtailed or eliminated, not because they have a different religion.
The U. S. Constitution in its First Amendment guarantees freedom of religion: one is free to practice the religion of one's choice, or refrain from the practice of any religion.
Now if Islam were a religion like Buddhism or Christianity or Judaism, there would be no problem. But Islam is unique. On an extreme view which I do not endorse, Islam is a political ideology masquerading as a religion; on a moderate view, which I do endorse, it is a hybrid ideology: at once both a religion and a political ideology. Either way is not a pure religion.
Qua political ideology, Islam is incompatible with Western values, or at least U. S. values. One reason for this is that Islam is not tolerant of religious diversity. It cannot be since it blends the religious and the secular and does not recognize the separation of church/mosque and state. Secular law is driven by Islamic law, or rather secular law just is Islamic law. So the 'infidel,' whether Buddhist, Christian, Jew, or whatever, must either convert or accept dhimmitude.