I've always had that problem with mustard and pickles. I don't eat either of them, and there are so many pre-prepared sandwiches that have them, as well as fast food burgers and sandwiches. With grab and go, I'm usually out of luck and can't use it - with fast food and ordering, I try to request NO mustard, NO pickles, but probably 1 out of 5 times one or both of those things are still on it. And what's worse, both of those items aren't the kind of things you can just scrape off - mustard is a very strong flavor and seeps into meats and breads, as does the pickle juice.
At least with mayo, I love it - so I'm good with mayo, aioli, remoulade, and any other combination. But I can sympathize with you non-mayo folks because of my mustard and pickle thing!