Experience teaches how to avoid packaging. For example, I had your mayonnaise issue with vinegar until I started making my own, which turns out incredibly easy and fun.

My bulk food store sells soy sauce, soap, and other things into containers I bring.

With mayonnaise, you might consider my solution for oil: stop buying it. I haven't used oil in years and eat a lot more nuts. Everyone's tastes are unique, but I love this trade.