I'd actually say it's significantly more political than most. It's a philosophy about the nature of political and economic power.

It's hard to get more political than a political philosophy. About the only way is to find one whose proponents are particularly debate-y and prone to infighting, and fond of byzantine governing arrangements to avoid entrenched or coercive positions of power.

Anarchism is typically focused on opposition to coercive or involuntary ruling arrangements. It's beenpoliticized as being in favor of chaos by people on the powerful end of said arrangements.
Because they're against hierarchy, anarchist social arrangements typically require much more political involvement than others.