The Spanish Civil war started as a result of a half-successful, half-failed coup by elements of the Spanish right and the Spanish armed forces against the left-wing government. The coup was crushed in parts of the country (including Madrid) but succeeded in a lot of areas and that formed the boundaries by which the war was fought.
In a lot of cases control over entire cities and regions were decided by activism of small groups (sometimes a few hundred or even in the dozens) of militant citizens by both sides. In particular, the port of Serville by which a huge amount of aid flowed into the Nationalist side was actually a left-wing stronghold whose working class was ready to fight against the military takeover but couldn't because they weren't armed. The guns and the bolts (they were bolt-action rifles) were stored separately in the city and they weren't able to get their hands on both. As a result the city fell to a relatively small number of coup aligned soldiers.
Let's say the Republicans do a bit better: the guns and the bolts were stored at the same place in the city: the working class and unions arm themselves and fights off the coup. Similarly, all over the country, the left is somewhat more successful and the coup succeeds in far fewer places. Germany and Italy sees the coup as an abortive failure and limits aid provide to Franco, by winter of 1936 most of the country is back in the government's hands and by spring of 1937 the "war" is all but over. Franco flees into exile to Italy and nobody pays much attention to him.
What happens next: the Germans and italians don't get to try out their fancy tactics and equipment in an actual war, a left-wing instead of a fascist government is in power. The Communists aren't nearly as strong because the Republic didn't need Soviet aid to fight Franco. How does this impact WWII?