Surveillance violates the privacy of common folk and thus is somewhat permitted, but violation of banking privacy threatens the rich and influential people and their (shady?) dealings, so that has always been restricted and actually enforced.
2) "A list of credit card transactions" is the kind of data that I'd assume that Visa/MC aren't selling to anyone ever, I'd expect any data sales to be on the level of "real time subscription to how (and how much) different demographic groups are shopping in company X or in location Y", but not on the level of individual transactions or individual accounts. Group them by zip-code and hour and you're fine even for GDPR requirements; and you can provide "individual" granularity for the merchants (e.g. for stock traders who want to predict revenues) since merchants generally have no privacy protections.
ico[1] is a useful resource for all GDPR related questions, but to answer your question: yes. Under GDPR, "personal data" is "any information relating to an identifiable person who can be directly or indirectly identified in particular by reference to an identifier."[2]. You can also read the "Article 4 - definitions" section in the official regulation doc (pdf)[3].
For the most part, GDPR protections for "personal data" only apply to identifiable data, as would be expected.
1. https://ico.org.uk 2. https://ico.org.uk/for-organisations/guide-to-the-general-da... 3. http://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX...
Technically, writing "John Smith" on a piece of paper can become anonymous data if there's no way to determine who wrote it and it doesn't mean anything to anyone who has access to the piece of paper (because there's a lot of people with that name or because they don't know anyone by that name) but of course names should be treated as personally identifiable to be on the safe side.
On the other end of the spectrum a vague description like "that chubby guy with the crew cut" can be personally identifiable information if you know who it refers to, even if someone else might see it and have no idea who you mean.
So the exact lines are highly contextual and pseudonymisation does not guarantee anonymisation: if you call a Rose by any other name, you still know it's her you're talking about.
I don't have a good idea idea how legitimate a credit agency's legitimate interest really is. I might set aside some popcorn for seeing how this particular issue gets resolved.
Furthermore "please delete my data" doesn't really mean "delete all my data", it means something like "I revoke whatever consent I gave and delete all my data that you now have no right to use" - so the company is allowed to keep all the data for which the GDPR gives them a right to use without your consent.
I've lived in both the UK and USA and used credit products in each, and your access to such credit appears to me almost entirely determined by a handful of credit reporting agencies "scores" in both countries in a pretty similar way. Heck it's even often the same company - Equifax (one of the largest) operate in the UK as well.
1) There's no "EU score", each lending market is somewhat separate. Past history in one location may or may not influence your score in another location.
2) Instead of a general/universal "credit score" calculated by an agency, there's often a concept of "credit history" which (depending on the country) may or may not list the amounts of existing loans, of previous loans, and history of late payments. The difference being that instead of lenders getting a score calculated by some agency, the lenders get the data and make their own decision, with possibly very different opinions on which factors are important. Not everywhere, of course, some countries (e.g. UK or Nordics) are more like USA.
3) The process tends to be highly regulated. If you're providing factual data as opposed to an opaque score, each item better be correct - distributing to all lenders "Bob defaulted on a loan in 1999" is libel if it's not true; the dispute process tends to be more consumer-friendly than USA - e.g. a requirement to remove the disputed items immediately and return them only if the debtor can prove its validity), maybe a requirement to expire entries of missed payments within x years, etc.
4) In some countries, that agency is run by the gov't, i.e. purely a central official registry of loans and/or bad loans, which is somewhat sufficient to verify creditworthiness. In others, it's like Equifax.
5) There often is a principle that the credit reporting agencies can't give/sell that data to anyone - you must give explicit permission for every company before they can gain access to that data.
6) In many countries there's no concept of "building credit" - where there only information provided is about negative events (e.g. defaults or missed payments), so having never taken a loan combined with good income gets a perfect rating, as it's not distinguishable from a long credit history and having never missed a payment.
So it's quite tricky - similar but different.
On top of that, I don't think there's anything in the GDPR limiting it to internet related things, so brick & mortar stores will have to be compliant as well, afaik.