Refers to a person who agrees with or supports a political or ideological movement, often without being an official member. Can carry a slightly dated or political nuance.
He is a sympathizer of that political party, but not a member.
Compound of 共鳴 (kyōmei, 'resonance, sympathy') + 者 (sha, 'person'). The term likely emerged in the early 20th century to describe political sympathizers.