Please read the entire article before clicking on any of the links, and I’ll explan why.
We’ll start with VISA, which has an opt-out form. Remember you’ll have to do this again for any new card number you get, and take the time now to add it to your calendar to do again in 4.5 years, as they require a renewal every 5 years.
Mastercard also has an opt-out form, but read on first. I don’t see any time based renewal requirements, but remember to add any new cards you get. Most notably their wording states “opt-out from our anonymization of your personal information to perform data analyses” which suggests you’re opting out of anonymization. It appears that you can perhaps only properly opt-out if you’re in the EEA or Switzerland.
AmEx also has options to opt-out, but they make it more difficult than a simple form like the above two.
What’s notable here is that VISA or Mastercard but a speculated narrative is that VISA and Mastercard do not know the full identity of the card holders, only the card issuer (ie your bank) does. This is different from AmEx who is the issuer and processor, so they get all of your information. What’s notable here then, is if you go to their opt-out website from your home computer or phone, they can legally record this information, and map it to your credit card number you’ve just used on their opt-out form. So if you do go to their opt-out website, you should use a browser like tor that masks your origin — but I see that Mastercard has already blocked you from anonymously opting out using tor.