Not necessarily illegal: citizens from Schengen signataries don’t need any kind of visa, nor a passport if their country issues picture IDs to all its citizens, but they may not have the same vaccination schedules; there are a bunch of other international treaties which mean you need a passport but no visa, it’s basically a case of “buy a bus/plane ticket, hop on and go”. And you have “emigrant returns”, children or grandchildren of emigrants who either have double nationality from birth or the right to request it and whose country of birth may again have a looser vaccination system. For example, I have no idea how good the Peruvian vaccination system is, but last week I got a visit from a door-to-door salesman who was about to celebrate his first in-Spain Christmas and who proudly showed me his Foreigners ID Card marked “EU System”: his wife’s grandfather was a Spaniard, so she was able to obtain the nationality by proving that, and her husband counts as a “EU citizen” for immigration purposes even though he’s Peruvian (he doesn’t need a work permit, gets a speeded-up nationalization process).