One problem with utilitarianism (at least as defined by Mill) is that it states that the best action is the one that creates the most happiness, of the highest quality, for the greatest number of people, in the long run.
This kinda sounds like a good idea, till you realize that clauses like "for the greatest number of people" is, implicitly, a justification for letting some people fall through the cracks.
One idea that underlies a lot of anarchist thinking is that any social structure that automatically, arbitrarily disempowers or excludes anyone is fucked up.
So, that's one way in which the two are, potentially, fundamentally incompatible -- much less either one being able to provide any sort of justification for the other.