Guinea-Bissau war of independence. | AskHistorians Archive Observer

This happened during a realignment in Brazil's foreign diplomacy during the 70s.

Brazil's foreign diplomacy during the 1970s was mostly aligned with the "Capitalist Bloc", led by the USA and its allies. Brazil was living under the military dictatorship regime of 1964-1985, which justified itself and its measures (like torture, restriction of political rights of leftists, etc) as necessary to defeat communism during the Cold War. So Brazilian relations with the Soviet / Eastern bloc got colder, after they had thawed under the previous regime (and especially during Janio Quadros and Joao Goulart presidencies, 1961-1964, with their more "pragmatic foreign relations". The vice president Joao Goulart, for example, was visiting the People's Republic of China when Janio Quadros resigned and had to face many difficulties returning to Brazil).

So why was Brazil one of the first countries to recognize the independence of Portugal's African colonies, even though many of them came under the control of Marxist political parties?

This happened during Ernesto Geisel's presidency (1974-1979). Brazil's military dictatorship was initially aligned with the Portuguese dictatorship due to ideological reasons, and also cultural ones. But notice that BRazil and Portugal never actually had that "special relationship" that the USA and UK share, for example. Power projection of both countries was much less than their Anglo counterparts, so this support is mostly translated into support in the UN and ease of Portuguese to immigrate into Brazil. But president Geisel could see the way in which the Portuguese African revolts was turning, with Portugal more and more likely not to keep its colonies. Geisel then assumed a pragmatist foreign policy and recognized the independence of the new African nations that shared (at least partially) the same language as Brazil, with the intent of creating greater economic relations with them.

This worked in the case of Angola, for example. Even though it was ruled by the Soviet-backed MPLA, Brazil was the first country to recognize its independence and Brazilian exports to Angola increased from US$ 6 million before its independence to US$ 26 million in 1977.

I don't know the exact reason for Guinea Bissau, but it's probably the same as for Angola and other Portuguese African colonies.

In English I think the best source you can find to discuss this is:

Jerry Dávila. Hotel Trópico: Brazil and the challenge of african decolonization 1950-1980. London: Duke University, 2010.

If you can read Portuguese, this is a good source as well:

http://bibliotecadigital.fgv.br/ojs/index.php/reh/article/view/2561/1520

Pio Penna Filho; Antônio Carlos Moraes Lessa. O Itamaraty e a África: as origens da política africana do Brasil. Estudos Históricos, Rio de Janeiro, n. 39, p. 57-81, jan./jun. 2007.