I can understand that, but in this day and age of formula that doesn’t need to be refrigerated after mixing and ziplock bags for solids it’s pretty easy to have food in the diaper bag that’s pretty obviously not stolen. And I remember my mom doing the same thing you’ve done. When it came time to teach me a lesson mom would just take me home, all plans canceled, time to go. Of course that’s a beyond 2 year old thing, they need a bit more language skill before you can run that chain of association of how we’re not going to do this thing they wanted because they were a pain at some other stop.
Not sure if you're an experienced parent or not, so I'll just add that most formulas need to be consumed within 2 hours of mixing, or refrigerated for a max of 24 hours before they are no longer viable. That may depend on the type of formula, which can be entirely dictated (and usually is) by what a given child will tolerate. In most cases 2 year old children (or even 1 year olds for that matter) are not drinking formula or any prepared milk type foods, they drink whole milk, which tends to go rancid fairly quickly at room temp.
Obviously stolen can be subjective even when you have ziploc bags - consider that anything can be removed from any package food-wise (at least reasonably sized food items you would give a 2 year old child anyway), so those could indeed be stolen, although it would be much less obvious that they were (the initial outward assumption of most people would be that they were not stolen), so that point is well taken, but not necessarily a panacea to the initial fear.
"When it came time to teach me a lesson mom would just take me home, all plans canceled, time to go. Of course that’s a beyond 2 year old thing, they need a bit more language skill before you can run that chain of association of how we’re not going to do this thing they wanted because they were a pain at some other stop."
That's the option I have as well. Quickly finish shopping and go home if need be. Most often; no matter what, I have to get what I initially went for regardless of how badly my child is behaving. I lay down the law, strap her into the shopping cart, move quickly and try to ignore the crying and finish the task at hand (some people would perceive that as ignoring my child), but I would've already disciplined her and moved on. How are they to know that occurred? Is it my responsibility to them to persuade them that I had already dealt with the situation as best as I could and she has already been punished/disciplined/dealt with? I think that's the crux of the problem - a lot of people make a lot of assumptions based only on what they immediately see. They don't stop to consider that some of the people they perceive as ignoring their children are actually following up on disciplinary action already taken. Sometimes the best way to deal with unruly behavior is by not feeding the behavior with further unwarranted attention (be it positive or negative), especially if the behavior has already been, or attempted to have been corrected (why belabor the point with a child that won't get anything out of further reprimands?).
Sorry for the long-winded reply...