The major source of anti-semitic slurs are assimilated Jews. As they assimilate further they will no longer see themselves as at all connected to Judaism, and like most Americans, will leave us alone.
The Israelis aren’t so lucky, as the zionists have nothing to assimilate into.
By saying we are “American Jews” (with “Jews” as the noun) rather than “Jewish Americans” it suggests we were Jews first, are now in America, but will be somewhere else in the future, but will always be Jews. While we may happily live in America for a while (centuries, millenia, etc.), at some point in the future we will be elsewhere.