In the US, your religion should not have any impact on admissions.  However, there are always random situations in which your nationality may have implications, such as being from iran .  

While this was reversed shortly after, and in the case of iran should stay stable as the new talks between USA and Iran have opened borders more, it shows there was at least enough prejudice from an academic university to push it through.  I mention this specifically as it was not a government block as the other answers have pointed out in terms of visa.