While most progressives today disavow actual communism, those that care about the history of ideas still typically regard Karl Marx as an important and serious thinker. And his idea that has had the most influence is dialectical materialism, or the idea that the only driver of history is socioeconomic forces.
According to this view, religions, philosophies, ideologies, worldviews, and even culture at large are simply illusions, embraced after the fact to justify this or that move in our class warfare. Marx’s views of history were influenced by 19th century evolutionism. Think of the idea that we’re just genes trying to reproduce: You may think that you’re in love, or that you do your work for some higher purpose, but really it’s just your genes tricking you into thinking that to increase their odds of spreading. Hence, for example, his notion that religion is just “the opium of the people” (a quote which is much kinder to religious believers in its context than is usually thought, by the way): beliefs have no influence on history.
This is why progressives view redistribution as almost a holy duty: If everything is about dollars and cents, well, everything is about dollars and cents. Conservatives also believe everyone should have a good standard of living, but they also believe that if people achieve this through work they will attain a greater degree of human flourishing than if they just get a check in the mail, since people’s flourishing is not just limited to the material. That’s why we have more nuanced views about redistribution.