a. Devarim 7: 3-4 and Ezra 9 & 10, specifically prohibit intermarriage with pagans. It does not refer to other monotheists like Muslims and many Christians. Both religions do in fact believe in the God of Israel, so in the modern era, how does this prohibition still apply? b. Also, Maimonides seems to have drawn similar conclusions. He wrote that the purpose of Islam and Christianity was to spread monotheism and the knowledge of the God of Israel.
a. Many mitzvot are worded towards the paganism which was common when the Torah was given 3,300 years ago, but applies to all gentiles, as well, and intermarriage is an example (each mitzvah must be examined and learned in depth individually from the sources to ascertain in which case it applies). b. There is a huge difference between our recognition (!) of the aid Christianity and Islam supplied in spreading monotheism, Bible, and world-improvement, as opposed to Jews marrying (!) them! The latter could bring the end of the Nation of Israel and the 613 mitzvot, through assimilation, which would be a tragedy for humanity, for we still have a lot of world improvement ahead of us. This also is the rationale behind the first answer (a).