Modulo MLs defining state to mean "any method of organising a society" in which case not even anarchism is stateless because yes of course we're doing that. The common politological understanding of state is more or less along those lines, too. I propose to not get anything in any twists over definitions.
Anything is only incompatible with anarchism insofar as it inflicts hierarchical power. Certain stuff at least some people call communism most certainly falls under that umbrella (though even Lenin admitted it was state capitalism), others are compatible or at least very close. Classical council communism certainly looks awfully like anarcho-syndicalism.