The Spanish Civil War was one of the great mythical wars of modern times. People everywhere, and especially abroad, saw what they wanted to see. (pg 205, Jose M. Sanchez, The Spanish Civil War as a Religious Tragedy)

I find the above quote to be an apt description of much of the historiography of the Spanish Civil War. Often a writer's bias will heavily influence their work. This is especially true for the writers that made their arguments shortly after the war, as most of the more recent writers (like Thomas, Preston, and Beevor as well as the aforementioned Sanchez) are more evenhanded with their analysis. However, there are exceptions from every political persuasion that continue to analyze the Spanish Civil War with a biased lens (often these biased writers are also not trained historians).

And why does it seem that so many historians have such varying opinions about it?

I would argue that the above quote and my above analysis is the answer to this particular question. The Spanish Civil War included nearly every political movement in the 20th century, which encourages analysis. Sadly most of that analysis minimizes or ignores the reality of the specific situation in Spain in favor of pursuing an ideological bias of some sort. Preston points out that the Spanish Civil War has generated nearly as much scholarship as has World War Two, despite its geographic and temporal confinement. Ideologues of all kinds continue to re-fight the Spanish Civil War in all kinds of media.

through my limited reading of other sources around the War, which aren't focussed on Anarchy, it doesn't seem to be a major factor

While you are correct in pointing out that anarchism's impact on the war can be overblown, be careful not to minimize its importance too much. Not only was anarchism in the Spanish Civil War an important real world trial of the theory, it was also a very important part of the Republican faction. Anarchists controlled large areas of Spain and contributed heavily to the Republican military. For instance, you cite communism as 'far more serious' an issue, while I would argue that communism's importance to the Spanish Civil War has been overblown by many--including both sides of the war. I don't mean that as a criticism of your question, but rather I point it out to discourage the minimization of any of the major factions in the war.

I haven't studied anarchism in Spain enough to go into detail as to its success or failure. Preston presents the economic results as a mixed bag--improvement in some areas and abject failure in others. Output for some factories increased while others came to a standstill. Some crops rotted in the fields rather than being harvested, while other large estates were broken up and fallow land was used to increase food production. The analysis of Thomas and Beevor is largely in line with that of Preston.

Sorry I couldn't be more specific regarding anarchism's success or failure, but followup questions from OP and others are always encouraged.