How does activist non-participation accomplish anything when it looks no different from apathy to an outsider?

Indeed. From me to not show up in the polling place is as strong evidence that I don't endorse democracy as is evidence that I can't be bothered to because I don't care either way/I'm a selfish CDTist and think my vote is too unlikely to change anything/I'd rather go shopping or something. The way to show that you don't endorse democracy is to go to the polling place and spoil the ballot.