It's super simple...
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Yeah, I would absolutely expect someone with a sign of this style to call every single instance of genocide "The Holocaust". That's precisely the level of historical literacy I'm used to seeing from middle-class weirdos who buy these things.
I feel like you're getting a bit semantic. A holocaust vs THE holocaust are pretty close and the meaning gets across.
I’m used to seeing from middle-class weirdos who buy these things.
so what kind of weirdo are you having to somehow felt the need to put the world "middle-class" in here?