Of course algorithms drive political polarization (though indirectly)
Because online marketing is the business model of Facebook et al, and probably more profitable than selling drugs.
If marketing did not work, social media would not be so hugely profitable. There is a fundamental reason for existence of a lucrative ecosystem of SEOs and social media agencies around the networks. Just check job offers and above average salaries in social media marketing.
Intentionally or unintentionally those companies become ministries of truth, because what users see, read or buy is heavily manipulated by third parties. Even if the algorithms were not designed for it. Examples: fake reviews, sold back-links in search, fake views, likes, bot accounts and comments. It is not a coincidence that some countries employ whole armies of online trolls. They would not do it, if this did not work.
Then there is a whole army of influencers, who discovered that stirring polarization is lucrative. Because people love scandal. Online tabloid journalism.
The counter-measures should focus on tracking authority propagation, not information itself. That is: who said what and where. How authoritative was the source. Then who back-linked, liked or reposted a message. Unfortunately this information is typically non-public.