No African campaign, no Yugoslav campaign, and no Greek campaign result in an earlier Barbarossa, which will still be a meat grinder, but one for which the Soviets are far less prepared and whose logistical challenges the Germans are better quipped to meet.
Can this meme die? Not only - as PhillyofDelphi pointed out - Germany needed time to reorganize its army in several fields, from command to supplies; but the Spring Rasputitsa of 1941 was exceedingly long and brutal, which means that if Hitler insists on Barbarossa starting pronto, undersupplied and disorganized tanks are going to drive right into a ton of mud. If the Führer decides to go on, WW2 might end
earlier than it did historically.
A neutral Italy kind of requires them not to invade Greece as that aligns them too closely with the Germans in British eyes. If they don't (and that's a huge stretch) then you have to ask what will they do in the war.
I think that will depend on what Germany does. Without an Italian intervention then Germany doesn't have an skin in the Med game. if it pushes too hard in France (occupation and bases in Vichy zone to allow subs to operate in Med) then it's likely Vichy will be still born and the whole of the French empire is Free French. In this case Italy is even more hemmed in by "Allies"
If Germans don't have any interest in the Vichy zone then unless Italy wants to take on UK in North Africa and/or Greece (which will make it non-neutral as above) it is stuck.
Can't see Germany getting involved in any Balkan adventures from any of its co-belligerents then either.
So Italy has basically sat in a corner throughout the world war until it declares with the Allies right at the end and probably gets an occupation zone in Austria.
After that it's going to mirror Spain and Portugal. The only difference is Libya which may (as others have said) become Italy over the sea (as does Albania). If Italy does hold on to Albania and Libya (which is a stretch but possible), they become seriously richer in the 1950's and 1960's. Won't be founder member of EU until fascism is done but can see that disappearing earlier than Spain in otl.
If Italy is neutral, it's neutral. Greece was an attempt to one-up German successes in the war, as Mussolini feared being considered a junior to Hitler; if, for some reason, enough distance (re)forms between the two to keep Italy out of the war, then Greece is "safe" - for a certain value of the word. There might be some attempt at strong-arming, but not a whole invasion.
And as others have said, Libya - especially the coastline - would probably remain Italian. The native population was laughably low, and Italy had been pushing colonization
hard. If oil pops up early enough, this would only make the flow of settlers into a flood. The rest of the colonies are probably going to go at some point, with varying degrees of Italian influence.