Soap is an excellent cleanser because of its ability to act as an emulsifying agent. An emulsifier is capable of dispersing one liquid into another immiscible liquid. This means that while oil (which attracts dirt) doesn't naturally mix with water, soap can suspend oil/dirt in such a way that it can be removed more efficiently than using just water.
It's also highly recommended to wash all your produce / vegetables with 'produce washes' to more effectively remove pesticide residues.
Produce washes, which I assume you are referring to the kind that you spray onto produce and then scrub and wash off, are citrus based. I use them all the time to wash produce. There is no soap in them at all because most people would gak over the thought of eating soap or soap residue on food. The citrus acid in the wash will dissolve any waxes on fruit and wash away any nasties on the surface.
As I have stated before, I am also extremely sensitive and have never used soap to wash anything I eat and haven't had any issues. The vast majority of people who report a reaction to legumes are just having trouble breaking down the sugars in the legume. This is why we have products like Beano on the market. The reaction is the same as a gluten reaction.....gas, pain and even diarrhea. You can also be intolerant of them and that may very well cause neuro symptoms in some.