Having been based in Europe for the last 6 months with only US credit cards, I have some experience here.
Once you enter a US Dollar billed credit card, Ryanair switches over to quoting the final price in US Dollars. They also provide the exact exchange rate they are using and allow you to unselect the currency conversion and accept billing in the local currency (whether EUR or GBP or whatever it happens to be).
The checkout page clearly says: "Your debit/credit card will now be charged $ xx.xx (€ xx.xx) Click here for more information on our guaranteed exchange rate."
Clicking on the link then provides this information: "Exchange rate of 1.2402969 so xx.xx EUR = xx.xx USD. If you do not wish to accept the exchange rate please untick the checkbox below."
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