A sympathizer is someone who agrees with the aims of a political group, movement, or cause, and quietly supports it — but is not a member, and usually is not doing the work. That gap is the whole word. A member joins; a sympathizer approves from the side. During a strike, the workers are members of the union and the sympathizers are the people in other jobs who think the strike is right and will say so.

Here is what a dictionary line will not tell you: the word is almost always used by someone who dislikes the cause. Governments talk about rebel sympathizers. Wartime newspapers talked about enemy sympathizers. Police reports say 'known sympathizers'. It is a word of suspicion, and it has a specific and ugly history — in many countries, being labelled a sympathizer was enough to lose your job, your passport, or your freedom, without anyone having to prove you did anything. Taiwan's own martial-law period had this exact pattern. So when you write 'sympathizer', you are usually standing outside the group and pointing at someone.

That means people almost never call themselves one. You say 'I support them' or 'I'm on their side'. If someone does say 'I'm a sympathizer', they are being careful — marking that they agree but have not joined.

Though actually — there is a small neutral corner. In writing about history and politics, sympathizer can just be the accurate technical word for a category of person: 'the party had perhaps 40,000 members and several hundred thousand sympathizers'. No accusation there, just counting. And in older or gentler English you will occasionally meet it meaning simply 'a person who feels sympathy for someone in trouble', with no politics at all — that use has largely faded, but it survives in phrases like 'she found no sympathizers in the room'.

Spelling: sympathizer in American English, sympathiser in British.