Given European data protection laws, which are premised basically on the notion that computer files on individuals are presumed, unless proven otherwise, to be intended for helping the Gestapo round up victims for the concentration camps, the rationale behind this petition would seem to be almost a no-brainer from that perspective.
Americans, however, tend to be inculcated with the value that obeying the law comes first; the political institutions of the United States have had a continuous history dating back before the end of Negro slavery, and, thus, the basic principle that people can't be convicted under retroactive laws has prevented people who committed crimes against humanity during the period of segregation from facing prosecution in the same way as many Nazis did at Nuremberg.
And after 9/11, it would not surprise me if many Americans feel that while in hindsight rounding up the Japanese into internment camps after Pearl Harbor turned out to be unnecessary, this time something similar would only be a simple and rational precaution that only an excessive irrational emphasis on equality is preventing.
After all, real people, innocent people, died in the Beltway sniper attacks, at Fort Hood, in the Boston Marathon bombings, in San Bernardino... and that could have been prevented if this was done. What's a little inconvenience compared to actually saving lives?
Of course, the war with Japan was over in a few years; it is not clear to me when Muslim Americans would actually be considered safe to release from the internment camps, and so even if one didn't find such a thing diametrically opposed to American democratic values it would still be obviously wrong to people of a wider range of political views. But it's not surprising to me that at least initially, before reflection sets in, the notion is not without appeal to a segment of American society large enough for that to be distressing to many.