Does the GDPR entitle me to refuse to show my boarding pass at EU airport shops?

Certainly, in the UK you can refuse. This has become common practice since the public found out the stores were pocketing the 20% sales tax savings with out sharing.

Here is a link to the British newspaper which claimed to have exposed the scam.

https://www.independent.co.uk/money/tax/airport-vat-scam-five-things-you-need-to-know-about-the-boarding-pass-rip-off-10456609.html

Even before GDPR my experience is that when I say, "It's not necessary, my destination is also within the EU," then the checkout assistant doesn't push the issue. I've even had one reply, "It's ok, you don't have to show it if you don't want to"; I think that was in a Boots in either LGW or STN.

So the answer to "Can I refuse to show my boarding pass" is that you can, and you don't need to rely on GDPR when refusing. Even if you did want a legal argument based on privacy, the old Data Protection Directive has you covered with the principles of legitimate purpose and proportionality: if you're travelling within the EU then it serves no purpose for them to process your data, and it would be disproportionate to insist on it.

You can only refuse if the boarding pass is being read electronically. If the cashier just needs to visually see it, then GDPR does not apply. You can still refuse to show it, but then teller also can refuse to sell you the item.

If the system doesn't save your name (which is the only personal information on a boarding card - note, the frequent flier number is anonymized and doesn't come under GDPR) then I believe you also are not under GDPR rules.

Not sure if this is really worth the wrath of everyone else behind the line at the counter trying to get at the gate.

What is the goal here? Privacy? If you pay using your card, they already have more information about you than on the boarding pass.

Or can I at least demand an explanation of how my personal data is stored from the shop keeper?

They will probably refer you to their term and conditions, a website or some other printed brochure. I doubt the cashier or the manager is authorized to speak on corporate policy and procedure. Even if they are, they will probably pull you aside to speak to you.

So again, not sure if this is just a hypothetical question or something practical. I mean, really - isn't the point to overspend on something, get to the gate, and then regret it the entire flight? :-)

In the UK at least, Her Majesty's Revenue and Customs (HMRC) requires airport duty free shops (or "export shops") to be satisfied that the customer is a passenger or crew by demanding a "transport document" from the customer. This must show the current date of travel, flight number, final country of destination and the time of departure or boarding time. Simply put those duty free shops are not allowed to sell you duty free goods unless you show them a boarding card or airline ticket that has the required information. I imagine this is a "legitimate interest" for the purposes of GDPR.

The law is The Excise Goods (Export Shops) Regulations 2000: http://www.legislation.gov.uk/cy/uksi/2000/645/made/data.xht?wrap=true

More information here: https://www.gov.uk/government/publications/excise-notice-197a-excise-goods-holding-and-movement/excise-notice-197a-excise-goods-holding-and-movement

The airport shops that are not duty free shops ask for your boarding card or ticket because they can claim back VAT if you are travelling outside the EU, although not all shops pass this saving to the customer. You can refuse to show them the boarding card and they can refuse to give you the discount.

Martin Lewis did a good piece on the requirements and differences between the shops: https://blog.moneysavingexpert.com/2017/05/need-show-boarding-pass-airport-shops-video-guide/

Airport Duty free stores are mostly airside after security and in customs controlled zones where the country's customs officials require the retailer to prove where the products sold are being exported to. It's both for Eurostat reporting as well as the VAT and Excise reclaim. Hence the requirement for the boarding pass whether EU or Non EU.