"Internal criticism is silenced" is an... interesting view of the left. A more common view is that endless leftist infighting is one of the things that makes leftists ineffectual.
Insofar as that infighting takes the form of fighting over who is the most or trueist left, casting their opponents as not actually left, there is no contradiction here. The eagerness to use shibboleths, slips of tongue and anecdotal correlations to identify impostures who are merely pretending to be left for underhanded rhetorical reasons is an example of this. Crypto-fascists are the ultimate boogieman.
BTW it's not hard to find examples of the right doing this too.
Those are not contradictory. Without the ability to criticize others, different groups can each claim to be "the left", and they don't have the ability to work through their differences to unify.
