Yeah, I've been a bit hesitant to listen to that episode. The part quoted about about the "Dark Ages" is totally cringe-worthy, though. I'm not an historian and even I know that the "Dark Ages" is a mythological time that exists only in medieval fantasy books.
Well... kinda. There is a period between the fall of the Roman Empire and the First Crusade that is frequently referred to as the "dark ages" but it was called that more because for quite a while there was very little documentary history of the period. It was prior to the widespread adoption of Christianity and the subsequent proliferation of monks. But we have since found that the pre-Christian civilisations of Europe practised burial of grave goods, so we now have a lot of artefacts from the period.
Mind you, what you're referring to is a roughtly 100 year period. By 600, Christianity was all over the British Isles and the Celtic Christian monastic orders were all over Europe. The Hiberno-Scottish Mission, which founded abbeys all over continental Europe already started in 563. While some areas, especially Scandinavia, resisted Christianity until the 12th century, the vast majority of Europe was Christian not long after the fall of the Western Roman Empire.
I know all that--I was referring to the common idea that the Dark Ages were a period of no advancement of human knowledge. That's not technically true. Classical ideas weren't, to my knowledge, unknown to the Middle Ages, they were just shunned for the more acceptable Christian ideals. I've mostly learned the history of this period through the art of the time. If you look at the art the Middle Ages produced, it lines up with the Christian view at the time of 'this life isn't important/iconography bad/spiritual life more important'. It's not that Europe suddenly forgot all about perspective, it's just that their cultural values changed dramatically.
As far as I know, most Classical knowledge was lost for the Europeans. the Library of Alexandria was long gone and most of the Classical texts were only known in Arabic, which not many people spoke in Europe. The first non-Arabic version of the Almagest, for example, was only made in the 12th century. The Renaissance was partially kicked off by the rediscovery of Classical knowledge through Arabic sources.
Of course, there was a lot of close-mindedness. Europeans were hesitant to embrace the concept of zero because they first thought it was some kind of evil Muslim scheme. Christianity was a restraining factor, but not as big as people think as the Church didn't yet manage to completely invade the private sphere, that only really started around the Reformation, that's when the real religious zealotry started up. Medieval Christianity was a relatively lax and hectic thing. I mean, for example, in the 12th century, a French village decided to start venerating St. Guinefort, who just happened to be a dog. I have seen a medieval bust of the Virgin Mary, which had a carved mountain scenery on its backside, including a fellow who's merrily taking a dump at the base of a tree. On the back of the Virigin Mary. Pooping. And then there's the inclusion of pagan nature spirits in every single English church, without even attempting to Christianise them.
I think the real reason for the lack of science was, firstly the lack of knowledge about past progress, and secondly of a socio-economical nature. Generally speaking, rich countries excel in science and there weren't many of them in Europe. There were rich kings and nobles, but their puny little kingdoms did not have enough wealthy people with time on their hand to immerse themselves into scientific pursuits.
Also, mind you, the European states descended from the Roman Empire, which never really cared about non-practical sciences anyway.
And you can see a change in cultural values even in the realism of Greece and Rome--hell, even during different eras of Greece or Rome. Romans are famous for their ultra-realistic busts of emperors--they are generally older, stern, patriarchal. Whereas the realism of Greece reflected more their emphasis on youth as beauty. The art of the Middle Ages was more about allegory--realistic art was seen as decadent, sinful. The art was meant to teach lessons about morality and Godliness, not portray reality accurately. It wasn't a "step back", it was a shift of values. Just like abstract art of the early twentieth century wasn't a step-back for art, merely a different emphasis on what is valued in art.
I wouldn't say that realistic art was frowned upon, there's plenty of it in the Medieval period, for example look at this 11th century reliquiary:

Sensibilities changed, that's for sure, and the most realistic art genre, the monumental statues went out of fashion, but not because people said that they were ungodly.
Also, the vast majority of Greek and Roman art was also deeply symbolic and religious. It's just that we're so removed from that period that it's not obvious at first.