Ladies and Gentleman, call me Jesus-Christ because I am your savior and I have solved the production bug.

The bug comes when you're able to produce science, once you have learned Mathematics. I first solved it, and it turns out that the same bug happens when you're able to produce wealth in a city when discovering Guilds.

The solution is to allow to process science/wealth only when discovering a future tech (that is disabled in this mod anyway).
Only cons of this solution is that you're not able to produce wealth/science anymore in this mod (who actually gives a ♥♥♥♥, I finished all scenarios in Deity and have never once used those).

First you need to find the technology XML file (I'm on a Mac, but should not be hard to find on windows/linux), use "Go to folder..." in your Finder:
~/Library/Containers/com.aspyr.civ5campaign/Data/Library/Application Support/Civilization V Campaign Edition/MODS/A Mod of Ice and Fire (BNW)/XML/Technology/Technologies.xml

At the beginning of the code you should find this:

<Processes>
<!--Move Research from Education to Mathematics -->
<Update>
<Where Type="PROCESS_RESEARCH"/>
<Set TechPrereq="TECH_MATHEMATICS"/>
</Update>
</Processes>

Change it with this:

<Processes>
<Update>
<Where Type="PROCESS_RESEARCH"/>
<Set TechPrereq="TECH_STEALTH"/>
</Update>
<Update>
<Where Type="PROCESS_WEALTH"/>
<Set TechPrereq="TECH_STEALTH"/>
</Update>
</Processes>

You're good to go ! It should even work with saved games where you encountered the bug (if you restart the game after changing the code of course)