Programmer Humor

Anarchism is opposition to power hierarchies, specifically non-consensual or coercive ones. Wealth inequality without safety networks is a coercive power hierarchy, and so needs to be fought. Capitalism as a whole is almost always incompatible with anarchy, at least in the way we tend to do it now. In a system with strong social safety networks the choice to work for someone can actually be a choice, and so some schools of thought would view it as compatible.
Others view exclusive ownership of property as someone asserting power over someone else's ability to use said property, and therefore wrong. Needless to say, abolition of private property is not compatible with capitalism.