Agreed, I think the author's feeling towards this is commendable in spirit, but to let a generic phrase be forever attached to a political movement in any setting is a bit much, even if it's infamously memorable, it doesn't belong to Nazis.
Still, it's just a name change, so, aside from a few lines of code to change, it doesn't badly affect anyone. All power to the author

It's case-by-case. Fascists are going to invade and appropriate every shred of culture they can find. But some of their choice culture is so toxic that they will own it for a long time. "Final Solution" and "Concentration Camp". But others like "living space" are probably not forever nazi.