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I have no idea if you can use yellow or white onions in a recipe like this, but I don't see why not!
I also have NO idea why in the world every recipe has added sugar. I would make these and leave the sugar out. Who needs it and it certainly doesn't make a bit of difference to the pickling process. I'll bet they're better without the sweetness anyway. Who wants sweetness on a burger?? I also never understood why they put sugar in ketsup. How weird.