>If Obama's daughters (or Trump's if you are on the other side) were killed in some horrific racist incident, wouldn't you approve the usage of such software if it was the only hope of getting the perpetrator? Or would you say "as much as I am saddened, I cannot approve such massive invasion of privacy".

The latter, every time. The nature of principles is that they do not change with changing circumstances. I find your example extremely unpersuasive.