Either cannibalism is so objectionable that I'd refuse to patronize a restaurant that served human flesh, or I'd probably not mind them being cooked side-by-side.
That might be a bigger things for vegans, by buying even vegetarian stuff from burger king you're supporting a company that financially motivates a lot of actions you find unethical - that is logically consistent at least.
Interestingly I don't think it'd be the only logical stance for an ethical vegan - purchasing beyond meat products would signal the company of the increased relative demand of vegetarian substitutes potentially leading to that company investing more in beyond meat products and lowering their meat purchases, decreasing the market stability and liquidity for real meat products.