Well, language being a social phenomenon, neither pronunciation is incorrect according to any objective standard, since they are both rather common variants.

Is it “incorrect” that Germans call France “Frankreich” ?

What I'm curious to understand is how Iran and Iraq came to be pronounced differently in this guide (or otherwise), when they are both spelt almost the same way. The social phenomenon explanation, while I get it, seems too broad.

Because they aren’t pronounced the same in their respective countries/languages.

As mentioned elsewhere, Iran is “ee-raan”.

Iraq is more like “eh-raaq”.

They have different initial vowels which are obvious in Persian/Arabic script, but harder to translate into latin script with variable vowel pronunciations in English.

I don’t think there’s really a difference between “Iraq” and “Iran” for most Americans (other than, obviously, in the final consonant). Both pronunciations exist for both words, with the one that’s closer to the native pronunciation being more prestigious and the other one being often perceived as backwards or uneducated. (Nowadays, that is. I have no idea what the situation was in the 1940s).

It’s indeed surprising that the two are used inconsistently within the same book, but I suspect that’s just due to some uninteresting artifact of random chance. Perhaps the two sections were written by two different authors, or perhaps there was one author who happened to have an Iranian friend who exposed him or her to the native pronunciation. Who knows.