Oh hey, I'm the wife in this story. Having a fixed $/month budget for "things you buy at a grocery store" was doomed from the beginning. All the stuff in your house/pantry are on all kinds of weird replacement cycles that vary with usage and changes in habits. A monthly cadence also makes you sub-optimally plan around price movements.
An attainable goal is to reduce the average amount of monthly grocery spend and you do it by deciding, in advance, things you're no longer going to stock in the house, items you'll replace for cheaper options, or items you'll stock from wholesale clubs.
It's hard to bring the budget for gas down without people driving less. Your wife being the one tasked with filling up the tank is the messenger. It could be an emotional reaction as you describe but I would at least entertain the idea that her "bending the rules" is her way of trying to make an impossible ask doable. Whether she is consciously thinking about it or not, I bet the stuff that "doesn't count" aren't replaced every month and have spikey cost patterns.