[6] The party has also praised Osama bin Laden, the leader of Al-Qaeda, describing him as "an example of selflessness, conviction, disposition" in the struggle for "the freedom of his people".

[8] The PCO also argues that the Taliban ideology and practices are "an expression of the profound social backwardness of that people", it sees the need to support any movement of national liberation against US lead imperialism.

The PCO supports implementation of socialism, following the Trotskyist branch,[2] which they regard as the true form of Marxism.

The party also sees the impeachment of Dilma Rousseff of 2016 as a coup d'etát[13] and were also against Lula's prison in 2018, protesting for his liberty afterwards.

[14] The PCO is a staunch supporter of unrestricted free speech, asserting that the people should always be entitled to express their views and opinions, no matter how controversial, offensive or misleading they might be, and that any attempt of censorship will eventually result in the bourgeoisie controlling the public opinion.

The party is unique in the Brazilian left in its opposition to anti-fake news legislation and the criminalizing of homophobia.

The PCO is accused by various media outlets, rival leftist parties (such as PT and PSOL) and former members of being a cult and having cult-like behavior, due to the fact that party members seriously defend the ideas of their party, its founder Rui Costa Pimenta and his family (their ideas are considered by detractors as reactionary and very close to a personality cult, in this case a personality cult around the Costa Pimenta family, the founding family of the PCO).