I was hoping to finally get away from paying commission when shopping online.
Still, some of the retailers, e.g. British Airways are failing to process the payment when I specify “MasterCard debit”, it only works if I switch to generic “MasterCard”, which has a payment fee attached to it.
Do you know why this is happening and if it is going to be fixed in the nearest future?
It will soon be illegal for merchants to add these kinds of surcharges 
Take it up with the retailer. Often it will be down to an old BIN database and where BIN codes are not found in the database the system is designed to assume the worst and charge for a credit card instead of debit card…although some retailers are worse and if not found they just reject that card number range.
It is also worth sending a message to in-app support when you come across this, as they might be able to help or advise on how to proceed.
I’m curious, why do merchants charge more for credit cards than debit? Do they get charged a higher fee? And if so, wouldn’t their card processor be able to tell them exactly what fee that would be, so they can use that instead of relying on BIN lists which have a maintenance overhead associated with them (needs updating every so often) ?
Yes, interchange is capped at 0.3% for four-party credit and 0.2% for four-party debit. Three-party schemes (like Amex issued and branded by Amex) aren’t subject to these caps.
Processors can add any amount of markup they want, the caps are on wholesale rates. Most but not all processors charge more for credit, and often significantly higher markup (I know one merchant who pays 0.22% for debit and 0.9-something% for credit to her processor).
I don’t know if any processors can give the exact amount back in real-time.
I don’t think so 