I personally believe that preserving a false and misleading picture of reality designed to trumpet a deranged cult that is working to make the world objectively worse for everyone including themselves is not acceptable.
I would say, “Look mum I love you more than anything in the world but preserving some of these movies crosses an ethical line for me.”
Of course I grew up in a house of atheist jewish academics, so making and justifying personal ethical stances that contravene wider group stances is expected behavior in my family. And we take document preservation fairly seriously.
I got almost the exact same result using DDG on a cheap android phone. Within .1 bits of identifying info.