But I don't recall FDR ever saying "the U.S. is at war with the German people."  We were at war with the Nazi regime.  Likewise, we are at war with radical Islam (ISIS, among other groups) which is quite different from a war on all Muslims.

The ISIS propaganda quote is simply ISIS using peaceful Muslims as a human shield, and trying to characterize our attempts to ferret out ISIS threats as an attack on all Muslims.