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Here is the context:
“There are three schools of reviewing and two of them should be closed down. First, ...
Then there are those amateurs, often a rival (or, worse, a friend) of those whose work is under review, who grind in-crowd axes in public, to the bewilderment or deceit of readers.”
I know the idiom "have an axe to grind", but why "in-crowd", what does it mean? Does it have something with real axes? Thank you.
It means that the fights they are having are restricted to a very small audience (the in-crowd), so the wider public don't understand what they are reading.
But it is not about fights, it's about their way of reviewing books, films concerts etc. ("There are three schools of reviewing"). So how could they make review "in-crowd" (small audience) "to the bewilderment or deceit of readers" (large public)?
Its a bit like a private joke, those around who are not aware of the joke will be unable to share it.
'In crowd axe to grind' means that they are discussing issues that they alone know about in front of an audience who are not privy to these issues, therefore are unable to comprehend.
grind in-crowd axes 
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