On the other hand, there's this argument:
America is mostly a Christian country. We don't understand Islam and certainly not the ideological battle among its followers. Therefore we do not want to create big communities of Muslims which will, by definition, become a breeding ground for future soldiers of this thousand year old conflict.
We also don't want this war within the Muslim community played out on American streets, nor its sister war against the West.
There's also the treatment of women to consider. America civil laws supersedes all religion, period.
In the end it is our house. Although it is our policy and goal to welcome all law-abiding peoples, regardless of religion, it's difficult and even impossible to determine whether Muslim immigrants are moderate or radical, especially when moderate families can easily produce radical sons and daughters.
For these reasons and more, we choose to be highly restrictive and selective of all potential Muslims seeking entry, regardless of country of origin.
That's not the most unreasonable argument I've ever heard.