You translated Serge Eisenstein into English but he is universally known as Eisenstein. Eisenstein naturally was working under the watchful eye of Stalin so no time for revisionist history or accuracy. The film was one of the historical drama films of Eisenstein and the revised propaganda spin was developed with the Barbarossa German invasion of Russia in 1941. The enemy could easily be seen as the Finns?/Poles? initially as Stalin did not want to upset Hitler too much in 38/39. Most commentators usually say that the film is about the German invasion of Russia or at least a premonition of it but it is more to do with how Stalin wanted to be portrayed as the defender of the Slavs. Great propaganda and great art in this film's case can mould to suit different circumstances and different aspects of their masters. Addtionally Prokofiev's score is worthy of any concert hall.
The Crusaders were outnumbered by Nevski and had a very large contingent of Tartar/Mongols. Yes you are right the film is not an accurate history but a great film.