Having done a lot of research about what happened in 1932, and how anti fascism, Stalin, freedom, East Germany, Berlin Wall is related. This fact-check is an opinion based on historical facts, and tendencies.
The primary source they used is a Twitter account with even amount of followers, and following, a guy named Chris Abraham, no further information. Therefore, this fact-check, seems to me more like an opinion about the historical events. And, I am going to explain how this argument is an opinion.
"Antifa began as a 1932 Stalist front, not a freedom movement. Its 'antifascism' was anti-capitalism, and East Germany later used it to brand the Berlin Wall" - At the time (1932), the two main political views that were seen was fascism, and communism (known also as stalinism), Both opposite political views. Fascism stands for authoritarian, dictator leader, aggressive nationalism, anti democratic, and totalitarian ideology. On the other hand, communism stands for uniting all the working classes as one, democratic, and anti-private property.
With all these definitions being said, this argument considers anti fascism being anticapitalist, which was Stalin political position. And Stalin did this from in 1932 because of the Holodomor, a terrible famine that happened in the Soviet Republic of Ukraine that peaked in 1932-33, under Stalin's presidency. This is why this front was not a freedom movement against fascism, in the meaning of authoritarian mode of government, which restricted the freedom from their citizens, This front was mainly trying to make Ukraine's citizens not see all the damage Stalin's government has made.
Later, these political differences in the Soviet Union, both by Germany and Ukraine, were seen when the Berlin Wall was built taking apart East Germany and West Germany, both of them being completely different political views. Therefore, this part of the argument is completely true that they are influenced.
"Today's Antifa borrows the logo, not the ideals - silencing dissent in the name of justice. It fights fascism by imitating it" This second part of the argument gets trickier, because I had to look up how is Antifa related to nowadays politics, and I found a news' article in BBC.
President Donald Trump has signed an executive order designating Antifa as a "domestic terrorist organization". In the root of the radicalized ideas this organization provides, that is why is contradictory with being antifascist, because fascism is mainly authoritarian, leaving no room for opposition, which is exactly what this organization is doing, and the reason why this statement says so.
ANTIFA: https://www.britannica.com/topic/fascism
BERLIN WALL MEANING: https://www.khanacademy.org/humanities/art-1010/architecture-design/late-modernismpost-modernism/a/the-berlin-wall-as-a-political-symbol-edit#:~:text=In%20the%20late%201970s%20and,make%20their%20mark%20on%20it.&text=Thierry%20Noir%20is%20one%20of,existence%20in%20their%20daily%20lives.
FASCISM: https://www.ala.org/sites/default/files/2025-01/SRRT%20Pathfinder%20Fascism.pdf
STALIN HISTORY: https://www.britannica.com/place/Ukraine/The-famine-of-1932-33-Holodomor
COMMUNISM IN THE SOVIET UNION: https://www.oerproject.com/en/oer-materials/oer-media/html-articles/origins/unit8/communism-in-the-soviet-union
NAZISM/FASCISM:https://www.britannica.com/event/Nazism
BBC TODAY'S ANTIFA ARTICLE: https://www.bbc.com/news/articles/ced5gqn0p6jo