I suppose you could argue it's not uber-important what they thought about a war on another continent in which they had no direct stake, but all the other countries in Latin America couldn't afford to ignore it completely. See American Hemispheric Perspectives on the Spanish Civil War
Vargas was in favour of the Allies during the Second World War, and wasn't particularly troubled by a distant USSR. But did he follow Salazar in supporting the rebels, or just do nothing at all?
Secondary sources suggest the hostility Vargas had for the Soviets and communism and a strong Catholic influence puts his sympathies solidly in favor of Franco and the nationalists. Stanley Hilton uses contemporary US sources to suggest that the delay in recognizing the new Nationalist Franco regime was due only to a desire not to anger the US.(1)
Colin MacLachlan also argues that Vargas was under US and British pressure "keep a distance" from fascist powers, and that the temptation to recognize Franco compounded by Brazilian diplomats reporting on Republican atrocities committed against Catholic clergy.(2)
(1) Brazil and the Soviet Challenge, 1917–1947 by Stanley E. Hilton (Gbooks)
"The Vargas regime delayed recognizing the Nationalist government but only because, as the American embassy correctly surmised in September 1938, it did not want to 'displease' Washington." (page not listed on Gbooks)
(2) A History of Modern Brazil: The Past Against the Future By Colin M. MacLachlan
"The Spanish Civil War put almost irresistible pressure on Vargas to join Germany and Italy in recognizing General Francisco Franco's regime. Diplomats in spain reported every atrocity commited by republicans against the clergy. Vargas promised to recognize Franco once he captured Madrid and established effective control. In the face of pressure, Vargas managed to avoid agreements that limited his options, expressing support to be formalized at some vague date in the future." (109)
More from the primary sources is likely to be found in Portuguese language sources.
On the Brazilian political spectrum, Vargas was basically a "centrist" (during the 1930s). Like some other leaders, including President Roosevelt, he was caught between extreme right- and left-wing movements. Of the two, Vargas considered the left wing Communists potentially more de-stabilizing, so he mainly aligned with the right to crush the far left in 1935-36. Then he set up a dictatorship in 1937 that curbed the right as well (while drawing on its implicit support).
To the extent that he had sympathies for anyone in the Spanish Civil War, it was Franco. But he had too many problems at home to exercise strong convictions either way. Vargas did not give Franco a strong show of support, unlike Portugal's Salazar.
Salazar and Portugal were Franco's "neighbors." Brazil was not. That would cause the two leaders to act differently toward Franco.
During the build up to WWII (which of course includes the period within which the Spanish Civil War happened) Vargas oscilated, probably on purpose, between a closer alliance with the US and UK, and increased relations with the Axis. This was reflected in his cabinet, with, for instance, Oswaldo Aranha being a fierce Americanophile, and Felinto Muller a staunch Germanophile.
But about 1937, he was moving to the right, both internally (having staged a self-coup and rescinded political rights) and in foreign affairs (with many signs of rapprochement toward Italy and Germany). At that time, with the US and the UK being neutral, and France only timidly pro-Republican, there would be little reason for him to be shy about pro-Franco sympathies. This was certainly reflected in his propaganda, that systematically demonised the Republicans and blamed the war on the left and on democracy.
On the other hand, the complete unpreparedness of the Brazilian armed services, the long distance from Spain, the small importance of Spanish imports and exports, the absence of any real objectives to be attained by the Brazilian State in the conflict, probabably combined with a comprehension that the SCW was merely a rehearsal for a more important pan-European conflagration, would counsel him towards neutrality, to keep a good negotiating posisition for the years to come. So Vargas' position reflected these contradictory tensions. Militarily, he didn't contribute to Franco's war effort; diplomatically, he maintained an official pretence of absolute neutrality but dialogated with the Nationalists, not with the Republicans; commercially, he was happy to deal with an illegal uprising; internally, he used the conflict for his own ideological needs (and sternly repressed any pro-Republican positions within the Spanish immigration to Brazil).
