I have cruised three times so far and have never been asked to show my vaccine card. I have had it attached to my passport each time, so it was there if needed.
I suspect that they ask you to bring your card in case something goes wrong with Safe Passage. You also might want to have it if you need medical attention in a foreign country. And I wouldn't be too surprised to see some other countries (or cities within countries) introduce vaccine requirements for certain restaurants, shops, and attractions. So, best to just bring it anyway, I think.
I suspect this will be like the great passport vs birth certificate debate. A physical vaccine card is not required to board the ship; they just look it up via safe passage by scanning the QR code. Whether you need one depends on risk tolerance.
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