The Spanish Civil War was terrible for the country and its civilian population but in retrospect wasn't it fortunate for europe as a whole that the Nationalists won? I'm sure that the nazis wouldn't have tolerated a Communist/Socialist state on its western border after the war with Russia began. The Allies would have lost first Gibraltar and then contrrol of the Mediterranean and bordering countries; also supplies from the far east would have had to make the longer more hazardous journey via South Africa. It would have been much more difficult to help fight in SE Asia.
Sorry, I don't quite follow your reasoning. The German Nazis were supporting Franco's nationalists. But then Franco didn't get involved in WWII - at least, not overtly. And that's how we were able to keep Gibraltar throughout the war.
I think the contention is that Germany would have occupied Spain
However that's a slightly simplistic analysis
You could contend that to invade Spain the Nazis would have been forced to occupy South Western France too which would have stretched them too far for the Russian Front to have opened up with all that would have entailed.
As with most para history concepts there are an awful lot of possibilities and little way to test them
The allies probably encouraged the Italians to throw their lot in with Hitler by doing nothing to help the legitimate Spanish Government. They may even have encouraged Hitler by making him think they didn't have the stomach for a fight.