One way to hold effigy: somebody's shape, made on purpose in solid stuff. Stone, wood, bronze, straw, newspaper — the material does not decide the word, and neither does the workmanship. What decides it is that the figure stands for one particular person. Once it does, a crowd can in front of it or set fire to it, and it is the same word either way, because both are things you do to a person through their shape.
From the word’s history
Wiktionary gives effigy from French effigie, from Latin effigiēs 'likeness, effigy', from effingō 'represent, portray'. The root verb is about shaping something into a likeness, which is exactly what both senses require.
字源資料記錄 effigy 來自法文 effigie，再往前是拉丁文 effigiēs「相像的樣子」，動詞 effingō 是「塑造、描繪」。字根講的就是「把東西塑成某人的樣子」，兩個意思都少不了這一步。
Wiktionary/kaikki extract supplied in this evidence packet (source_ref kaikki:3f6f69a190036ae4:336459332): 'From French effigie, from Latin effigiēs (likeness, effigy), from effingō (represent, portray).'
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