Well, generally speaking demographic warfare has been pretty damn successful throughout history, and no less so in the 20th century. In the long run, he who f*cks most, wins. Today, the Africans are the only ones who are still doing it old school style: no battles to speak of, just massacre the women and children and in 20 years you win by default. But demographics are not to be underestimated, in any country.
When you say that a Muslim PM would be perfectly acceptable, well first of all I have my doubts as to whether that's just a statement, but in any case I don't think too many people would agree with you, particularly outside of the West, where tribal mentality is very much stronger. That's what it essentially is. My tribe, whichever one it happens to be, is preferable to all others, and given a choice I would choose to associate with and grant power to those who are of my tribe. When someone says that Islam is taking over Britain, or Mexicans are taking over the US, or Arabs are taking over Israel, it basically means "those damn no-good Other Tribesmen are gaining power, and we are loosing it, and if they continue to screw at a rate that exceeds our own, we're going to have problems a few years down the line. So, naturally, my sense of tribal (usually national) identity is offended."
Simple. Call it rascist, and it is, but it's part and parcel of being what has historically been identified as being human.