I've eaten meat a few times just to avoid making a scene. Got invited out to dinner by colleagues on several different occasions (diff people) and they were sushi and steak places. No vegetarian options. Such is life.
I manage to have positive impact with 99.9%.
So I can understand their point of view.
I'm not a vegan, or vegetarian, and I can understand that point of view.
So I don't understand how your comment is at all relevant.
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.
You're trying to bring logic into a moral decision. While I agree that that's the way I would approach it, it isn't the only way to approach it. As I said I'm a meat eater so I don't follow all the logical steps to being vegan, but that logical step I do understand.
Cooking the burger in beef/pork fat would likely be noticeable, but that is pretty trivial to avoid and _usually_ grills are crudely scraped down between different grillings, that will remove everything but trace amounts.
For the later case... I'm on board with sane things (don't fry veggie burgers in animal fat) but less with (don't prepare this food where meat products were prepared) simply because... I feel like the same amount of effort should be taken with each meal and vegetarians shouldn't require separate processing things.
To draw a parallel, I'm lactose intolerant myself, but I've always felt it's a bit silly that <GENERIC COFFEE PLACE> has separate blenders for milk/soy/other (except almond, due to the factor of nut allergies).
Vegans say this all the time. You can choose to be 100% consistent with ethics but how far do you take it? Do you shut out your family and close yourself off from most of society?
And a lot of people have religious reasons for not eating meat.