He accused some in the party hierarchy of "hypocrisy" over their concerns about internal groups running for NEC and office positions this weekend, in a column for today's Scotsman.
The Common Weal group has put forward a number of candidates, including MPs Joanna Cherry, Douglas Chapman and Neale Hanvey, who have signed up to a pledge for more democracy in the party.
Mr MacAskill said "complaints raised by some leadership figures" were surprising as such activity had previously been carried out by party HQ.
"Everything from explicit endorsement to financial support has been given to anointed ones," he writes.
"What’s fine for them is surely legitimate for others.
“Secondly, it also assumes that everything’s fine and any deviation from the official party line is, as they put it, ‘factionalism’. It assumes that such behaviour is almost 'just not cricket'.
"But this is the SNP, not the Communist Party of the Soviet Union or any of its satellite parties. Democratic centralism doesn’t apply. That was the euphemism for limited debate, but then ruthless central dictat.
"The SNP is a democratic party and there’s anger over many issues within the membership ranks and debate’s required. Much of this seems driven by fear of open debate and hence it’s being labelled almost as dissent."
The SNP has faced internal tensions since a rule change was implemented earlier this year that meant an MP would have to stand down from Westminster before seeking election to Holyrood.
The move was widely seen as a move to stop Ms Cherry, the MP for Edinburgh South West, moving to the Scottish Parliament. The party has rejected this, insisting the move came about to prevent a series of possible Westminster by elections.
The elections to the party's internal positions will take place this weekend.
An SNP spokeswoman said: "The SNP is proud to be hosting the biggest and most interactive conference of any political party during the pandemic.
"With five months until the most important election in Scotland's history, our agenda is focused on the issues of most importance to families across the nation."