Then they would be ignorant at best and poorly educated at worse.

They would be mixing up two entirely different classification systems. Functionally the equivalent of saying theirs no stars in the sky because water isn't wet.

Its just nonsense.

You would have to first educate them enough to understand the defined terminology before you could even consider them a peer in the discussion.

or what if they believe that there’s no north america, that there’s only one american continent?

THANK you i feel seen

In the first case, they're simply wrong, a country is a country. We might disagree on whether it is a sovereign state and worthy of establishing diplomatic ties. In the second case, they'll have to agree that the America continent has a part that is closer to the pole that a compass points to.