Is there dioxin in AeroPress paper filters?

No. The bleaching process used by filter paper manufacturers until the late 1980s used chlorine gas and the chlorine gas bleaching process created dioxin as a byproduct. In the late 1980s the filter paper mills switched to using what is called the non-elemental chlorine bleaching process (they use a chlorine compound, not chlorine gas) to eliminate producing dioxin as a byproduct.