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It did it at least eight times in my last game - even worse often showing ships that are NOT listed in the little "reference_card" supplied.

Surely there is no need for it to be even in the GOG version?
This question / problem has been solved by ConsulCaesarimage
The question pops up but it doesn't do anything. You can click on any ship and the game will continue without a hitch.

Anyway, if you want to have the full reference card, user srhill uploaded it on this thread: https://www.gog.com/forum/master_of_orion_series/master_of_orion_copy_protection_gog_pdf_lacks_images_drm_ruins_game
Ah, so it just the old ghost of the copy protection then. Good to know!
That screen caught me at off-guard as well during my first time playing the game. While it is confirmed any button can be pushed to proceed, there were a rumor that picking the wrong ship would still continue the game but sneakily setting the player at a disadvantage.

It makes me curious about the original copy protection. Are there any MoO1 veterans here who can attest what originally would happen if the ship was misidentified? Would it simply assign a new ship for the player to identify, or would there be something more to it?
Been a while as MoO was the first game I bought at GOG. A lot less hassle than the discettes (crooonx craaanx) but I think it kicked you out and deleted the autosave (save7).