Actually it is not impossible, and in the last few years there has been some anecdotal evidence of US citizens of Indian origin being denied visas. I know of one case involving a university student of Muslim Indian origin who experienced a visa rejection. His parents are Indian, he was born in the US, has never traveled to Pakistan, but could not travel to India to get married. No reason was given for the visa rejection. I have heard of other cases but really don't know much about them.

Similarly, many US citizens of Pakistani origin who have traveled to India in the past without any problems have reported that their visa applications have been rejected. Whether one wants to term it discrimination secondary to being a Pakistani or secondary to being a Muslim is, I think academic since one is largely a subset of the other.

Generally the people impacted by bureaucratic idiocy, whether it is based on religious profiling or is equally applied to all applicants are usually ordinary people just trying to conduct business, visit relatives or see some place that they identify strongly with.