It would only be socialist if the state ran it.

Quite right - that's one of the biggest mistakes people make thinking politically. Socialism and Communism aren't bad because they're ostensibly about sharing, cooperation, or being nice. They're bad because they're run by the government, who arrests or executes its citizens if they decline to participate in the government-run activity. If you've ever shared a refridgerator with multiple people pitching in to fill it with groceries, you've been part of a "commune" (lower case), which can be fine and great thing. It's when people aren't allowed to decline to participate in the commune without being arrested or shot that there's problems.

Yes what makes socialism/communism authoritarian is that it's almost always non-voluntary (ie they make you join the collective or else).

Exceptions to this are Kubbitzes (sp?) and small voluntary communes, which have their own problems but at least you can leave them!