While there are the Sport Club Corinthians Paulista of Sao Paolo, their logo looks nothing like the one on the wall there. Galatians FC is likely also a reference to the Corinthian FC, an English amateur team founded in 1882 and dissolved in 1939. Why is it significant? Corinthian FC handed Manchester United its worst defeat in history, an 11-3 beating.
That took place in 1904. The logo of the fictitious Corinthian FC suggests the team was founded in 1903. Likewise, in the Bible, Galatians immediately follows Corinthians. Additionally, the real-life Corinthians of Sao Paulo were founded in 1910.
I think it's also a direct reference to English football as well as Brazilian. The founders of Max Payne publisher Rockstar Games, Dan and Sam Houser, grew up in London.
I can't tell if they back a rival side of United's or if they're merely tipping their cap to football history, but the reference is obvious.
Above is a video providing some context of the run-up to the mission and its earliest stage. Payne is assigned to protect a Brazilian playboy named Marcelo, who evidently favors the Galatians, a team based in Sao Paolo. He's unhappy that the table at his preferred club has been given to Claudio, a player Marcelo implies isn't good enough for the European football leagues. Soon the game shifts to the Galatians' home pitch where, yes, a deal goes wrong, with attendant gunplay.