I feel like a lot of people derive their knowledge of Renaissance from high school history or at best history 101 because they focus a lot on change of thought on how thinkers operated (usually what's focused on basic history) and not at all in actual zeitgeist amongst commoners, the shift in nobility's status (and real birth of aristocracy) and how politics became much more worldly. Renaissance in Europe wasn't just how philosophers thought knowledge should be approached or extent of it, or how sciences were acknowledged differently from just theological recognition (I.E, writing down what is rather than exploring what could be), it was also change of social structure, politics both domestic and foreign and how the increase in wealth and urbanisation lead to development of interstate relationships. More concerning a RPG with adventuring party, how mercenaries, companies and aristocrats operated instead. PoE does an okay job as far as many of these are concerned, some details are nice such as economics, trade and the arms race but a lot is missing which is to be expected as it's first game in an original setting. Also D&D is as original as PoE is when it comes to supernatural, in that it's mostly just recycled mythology and folk tales mostly deriving from Tolkien but at least PoE does it in a setting that's frankly more interesting, early modern period and not late medieval.
I'm not sure I agree with what you're saying here, I might have misunderstood. I am from Florence (Italy), the city where the Renaissance itself was born. And let me tell you, PoE sends out strong Renaissance vibes from the setting; I do believe that Sawyer and/or other developers at Obsidian must have taken history lessons way beyond 101.
First of all, what do you mean by "the real birth of aristocracy"? Renaissance at its peak in southern Europe was incarnated by a myriad of powerful city-states in a continuous alternance between monarchy and republic. In Florence alone - despite what the Medici tv series and Dan Brown say - there were decades of republic, and even a theocracy. I believe the real birth of aristocracy lies in feudalism, which is already waning during the early Renaissance, so I don't get what you're saying here.
Speaking about the game, Pillars does a great job at recreating that period. The fact that a god took human form is a fantastic reinassance concept in itself. If you think about the art history, up until Giotto (early 14th century) and Lippi-Botticelli-Leonardo-Michelangelo later on, the figures of Christ, the Virgin or the saints couldn't even be portrayed as human, because they were untouchable, distant icons.
It's only with the Renaissance that the men started to "humanize" their idea of God, and they actually dared to portray Christ as a suffering man on the cross instead of a spitual being winning over death (Christus patiens opposed to the medieval Christus triumphans), the saints as humans, and the Virgin as a mother, for the first time showing female attributes (Maestà Ognissanti).
Waidwen becoming the human, living incarnation of Eothas is a Renaissance concept in itself, as are the gods talking like humans and feeling human emotions. The whole world of Eora feels like a 15th-16th centuries Italy, not only in architectures, and it does a great job at that.
I could go on with many other small examples, but seriously, if some players don't see the difference between the concept of this setting and FR, they are the ones who should be taking history 101.