“When you pay for something in the EU using your credit or debit card, traders and banks cannot charge you an extra fee – also known as “surcharging” – just for using a particular card. This rule applies to all card purchases (in shops and online) made within your home country or in another EU country.”
I think what the above is trying to get at, is that Merchants can’t charge you a surcharge simply because you are using a specific card (this is however dependant on whether you are in an EU country) - so for institutions like Monzo this may affect them as they are unlikely to go out and obtain a Banking Passport should a no-deal Brexit happen (I think).
As far as ATM fees goes I think @lumisota has put it right. I think you’ll still get charged the same over the £200 limit in say Spain as you would in New York.