The religious-iconography-knowledge of the "average peasant" is difficult to be certain about because we don't have direct accounts written by "average peasants".

We know that society was organized around religious themes and religious order, and the world was understood through a religious lens. The stained glass iconography in the Gothic cathedral would have been known and memorized, especially the stained glass paid for by the trade guilds. We know of the guilds paying for work at the cathedral because of accounts and ledgers. At places like Chartres cathedral, stained glass depicts the trades working, such as silk weavers. The work of the peasants was depicted as a religious endeavor, as the inclusion in the cathedral iconography would attest.

Furthermore the themes and symbols in Gothic architecture would have been crafted by "average peasants" too. Those masons and craftsmen would have certainly understood the icons and the associated narratives, but it is unclear to what extent craftsmen were a source of dissemination. We know the oral traditions were important, so perhaps the stories of the craftsmen were important, in addition to the direct teachings of the Church. One author, Emile Male, briefly describes an interesting narrative associated with icons in Gothic architecture, and how that narrative changed over time, like "Chinese whispers".

However, the "average peasants" would not be aware of relatively recent developments in "theology", like when more complete Aristotelian texts were introduced to Western Europe from the East.

I would conclude by estimating that the average Joe would have been able to tell something of every icon and symbol in the cathedral, and might even have a depth of knowledge about a number of icons and their narrative.

I hope I have been clear and helpful, and I'm happy to fix any oversights that might be found in my very dense post.