Back when Pepsi refreshed their logo, the reaction was mostly just people making fun of it. If they did the same now it seems like there would be anger.
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I sincerely doubt Steak 'n Shake tweeting "fire the CEO" was a serious call to action so much as it was jumping on the hate train for fun.
The framing isn't just that it is "woke", but, more to the essay, that they're destroying a classic American aesthetic.
They're very much making this out to be: it's us vs them, and mythologizing tradition. Equating corporate identity as American history does well to push corporate capitalism, but funnily enough, the logo only goes back to 1977. It's only as old as Don Jr!