Consider a webshop based in Spain (European union). After the buyer selects their country (shipping address) the prices are shown in the local currency, and only in that. However during payment, the credit card is actually charged in euros which are then converted to the local currency by the buyer's bank, using their own exchange rate. As such, you typically pay more than what is shown (at the moment it is a 3% difference). Also it makes comparing prices hard and gives them an unfair advantage. If the price is shown in my local currency I expect to pay that much. If the price is shown in euros, I know to apply my bank's rates and fees.
TL;DR: if they charge in euros, must they show the price in euros?