The one thing I can say in support of allowing Muslim immigrants: They have a much better chance of converting to Christianity here than they do in their countries (where they would face things like, you know, decapitation if they converted). Al Kresta had a segment last week on the huge numbers of Muslims that are converting (go to minute 9:00). It's the largest in history. Something is going on, almost like there has been a policy change at the DHS (Department of the Holy Spirit). Many of the converts report receiving visits from Jesus in their dreams. We think there are now 10 million "Muslim background" believers. By contrast, back in 1960, they estimate there were only 60,000. Read more here.
Most convert to Evangelical Protestantism, mostly because the RCC abrogated its missionary responsibilities in the 1960s in favor of social activism, but there are plenty of Catholic converts as well. One Catholic said he was approached by a young Muslim who simply asked him suddenly, "Can you tell me about Jesus?" So the Catholic told him about Jesus. The young man wept and said, "I knew it wasn't a dream." He said he'd had the same dream for 30 days, where a bloody man on a cross said his name was "Jesus" and "I love you."
It got me thinking, "What would I say if someone asked me that question suddenly?" Sadly, I think I'd be caught flat-footed. I've begun to give it some thought. Hopefully, I'll get that question some day and will be able to answer it well.