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Businesses already round to the nearest cent all the time. Any time an odd number is part of a 50% off sale, or any time you charge sales tax. The fractions of a cent are too small to matter, and we've gotten to the point where the pennies are too small to matter.
You say people will be pissed if you round up, but stores have been slowly increasing prices by dollars for the past few years and haven't lost a customer over it. A few cents of rounding isn't going to drive your customer base away. Especially if all the other stores are doing it too.
And just think for a moment. Let's say the store starts losing 4¢/transaction. The truly worst case where they always floor in favor of the customer. First, they could offset this by just blanket raising the base price of everything by 5¢ and no one would bat an eye, but let's set that aside for now.
Let's say a store does 10k transactions a day. Feels like a good average for a large sized store. That's a theoretical max loss of $400 a day. If the average grocery store customer is spending around $50, that's $500k of revenue per day for the store that just lost $400. I think that's pretty safely in the slush. Hell, they probably lose more than that per day on shrinkage alone. And they saved way more than that when they replaced all the cashier's with kiosks, and I didn't see any of those savings passed on to me.
No business is gonna fold over a 4¢/transaction loss. It's a negligible impact on your overall overhead. And even if it wasn't, the small bump in base price you would need to cover it is so small as to not register with your customer base.