Regressive because the new "tax" on the bread is a flat value, independent of the buyer's income and means. That's what the word means when it comes to taxes and fees.

And yes, eating to survive is kind of regressive in that sense, but it's not what I'm talking about. If we generally assume society is unfair but still balanced around current expenditures, adding more may upset that balance.

In the grand scheme of things, it doesn't matter whether any one particular fee or tax is progressive or flat or regressive.

It's the overall tax burden (or net payment, for poor people) of the whole system that's important for these kinds of fairness considerations.

The design of individual taxes should be more concerned with efficiency and deadweight losses.

That seems reasonable, a rise on prices of stable commodities can easily be counterbalanced by reducing taxes elsewhere.

I agree with that. But there has to be minimal delay between any expense and refund if you are making the up front cost higher for the lower income brackets. Waiting until the end of the year for a rebate won't be good enough.

I wasn't suggesting to give people a rebate for bread. Just the opposite.

Bread should cost whatever it fetches on the market (and that will include pigovian taxes, if any).

The amount and frequency of welfare transfers to poor people should be independent of how much bread they buy and when.

To give a concrete example: you get your welfare check at the start of the month, and the government doesn't whether you buy bread with it or noodles, and shouldn't give you a refund either way.