Leftism is non-theistic Christianity

It's also presentism. Trying to backwrite modern politics to the era of Christ is ludicrous. These kinds of statements generally tend to be advanced by people for a bit of shock value or people who are trying to 'strike a pose.'

Again, let's keep the focus on ideas, not personalities.

Democracy would have been totally alien to Jesus and his followers. They would not have been able to wrap their minds around the concept. At all.

The modern idea of democracy originates with the Athenians, through to Renaissance humanists, to enlightenment political theorists, without drawing substantially on Christian thought, and when they did, it was from forms of Christianity that were highly divergent from Catholicism, like Unitarianism.

While progressive Catholics embraced or adapted to democracy in the late eighteenth and the nineteenth centuries, and right-wing Catholics used democratic means in the twentieth, the Vatican was very reactionary and anti-democratic, and that wouldn't change until after World War II, and then, only kicking and screaming. There still is a deep streak of reactionary thought in the Catholic far right even till this day.

So, in all, modern ideas on democracy owe very little to Christianity as a whole, and practically nothing to Catholicism.

Modern feminism likewise owes little if anything to Christian thought. If anything, it was a reaction to Christianity, including Catholicism. While feminism was eventually embraced by progressive Christians, including progressive Catholics, anti-feminism is very much alive in modern conservative Christianity, both Catholicism and Protestantism.

Pacifism, on the other hand, did largely arise from Christian thought, but from a variety that was extremely divergent from Catholicism, or mainstream Protestantism for that matter. It's first proponents were the Bohemian Brethren, the German Anabaptists and Pietists, and the English Nonconformists, like the Quakers, largely in response to the countless Wars of Religion in the sixteenth and seventeenth centuries. Pacifism entered progressive Catholic thought in the nineteenth century, but didn't become widespread until after WWII.

As for the audio clip you provided, it's basically just a variation of the old conservative Christian trope equating political differences between the left and right as fundamentally religious in nature, and portraying their opponents as a heretical religious movement. It's pure claptrap, of course.

I didn't watch the TV series, but it sounds like a mix of exaggeration, distortion, whitewashing, denialism and boosterism. On par with Islamic boosterism that attempts to trace everything good about modern society to their religion, and everything bad as alien to it.

I don't have much respect for boosterism. It reminds me of the scene from Stand by Me were one of the boys defends his abusive father as a war hero. Real history is so much more interesting. Christianity, and Islam, for that matter, have indeed had a major impact on the formation of modern society, but not always for the good.

Whitewashing over the mistakes the Church has made in the past is fundamentally dishonest and a disservice to the Faith. We've arrived at where we are today because we were willing to learn from our mistakes.

Bellarmine was one of the few Catholic thinkers of his time that questioned the divine right of kings, as did a handful of other Jesuits. Though he was quite progressive for his time, his ideal political system was not democracy, though, but a sort of non-absolute elective monarchy with some rights devolving to the aristocracy, and also to the people.

Despite of what your book argues, it is a stretch to conclude that he had anything beyond a very distant and indirect influence on the development of modern democracy. About the only real link was that one of the main proponents of absolute monarchy, Robert Filmer, lambasted Bellarmine's ideas, and Thomas Jefferson opposed the theory of absolute monarchy proposed by Filmer. Also, both Bellarmine and Jefferson were humanists, and probably read a lot of the same classic literature. So peripheral, at best.

A more plausible link would be Charles Carroll, a Jesuit trained lawyer who signed the Declaration of Independence. He was the cousin of John Carroll, a disbanded Jesuit who would later become the first Bishop in the US. Both were rabidly against absolute Monarchy, and also quite at odds with the Vatican at the time because of the Suppression of the Jesuits. Neither could be said to be a representative of official Catholic teachings on the subject of democracy, which were very strongly monarchist at the time. Modern day Traditionalists would probably consider them progressive dissidents. John Carroll's brother was also a signer of the Constitution. Whether any of the Carrolls were influenced by Bellarmine is certainly plausible, though I can't find any evidence for it.