Well Nana needs to pull her head in, based on this scenario, the barista isnt the one who makes the decision. It is the cafe owner.
Accepting cash costs a business costs anywhere from 4.5% to 15%, not to mention the reduction in working capital as you need to carry a float in your till. That would be a minimum of $200 for most places, now add to that you need to buy a safe, deal with the headaches of keeping the cash safe(taking it to the bank or having it collected, which again costs money/time), the risk of counterfeit cash, staff theft, staff errors in cash handling etc
I think as long as it is clear it should be up to the business owner