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Because of certain dark parts of our history, this sounds too much like white superiority.

A more fair example would be is it wrong for someone to put "black and proud"

First, there's a lot of history of Christian supremacy, too. Many other religious groups were kept down by Christians and sects of Christianity, both in and out of this country. Second, there's a decent history of (attempted?) black supremacy, too, and even more black separatism. Third, I'm terribly offended by that double-standard that makes it okay for black people to be proud but not white people. It's not as if black folks are more racially homogenous than white folks; they come from as many different places, and very few of them have connections to their Zulu or Pygmy or Ethiopian or whatever heritage. Fourth, I think it's divisive. So, yes, that would be offensive to me in much the same way that "Christian owned" offends me.

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"vegetarian owned"

I'll admit that this wouldn't offend me, but largely because my reaction would be dominated with "huh?". I can't imagine that this would ever happen (unless it was for a restaurant or a granola-y type of store or unless cruelty-free was a part of their advertising otherwise, in which case, it'd seem relevant), so it's hard to fairly judge what a reaction would be.
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Bitt Faulk