The other thing that occurs to me along this line is that you have to be very careful about identifying someone's religious affiliation based on their ethnic appearance. I know a number of South Asians in this country who are Hindus or Sikhs - or even some who are Christians and whose family had been Christians in India, not simply recent converts. Many of these people are likewise in highly visible professional positions, and the Hindus especially can be hard to distinguish from Muslims from that area of the world. (And for that matter many Westerners find it difficult to tell the Sikhs from the Muslims - though there are a number of telltale signs if the individual observes their religion, if you know where to look. The Sikh religion is a syncretic religion quite different from Islam, and in many ways more compatible with a Western outlook).
Conversely there are quite a few Muslims who are of European or Chinese ethnicity, contrary to the stereotype.