Secular Jews at various times have handled Jewish holidays in various ways. 100 years ago, secular Jews of some persuasions in New York and Warsaw had Yom Kippur parties where they ate and drank, and where they especially ate not-kosher foods, as in the headline above from 1898. They sent a message to the others, didn't they?
Says Eddy Portnoy in Tablet magazine:
"What does one do, after all, when prayers and traditional customs no longer hold any meaning yet you still want to be part of a Jewish community? Eating with intention on a fast day allows you, in one fell swoop, to thumb your nose at the religious establishment and create a secular Jewish identity."
In Israel today, the whole country has shut down, without much push-back from the non-religious as far as I can tell. Said Haaretz yesterday: "Public opinion surveys over the past few years show most Jews in Israel observe Yom Kippur. A survey conducted by the Central Bureau of Statistics in 2009 found 26 percent of Israeli Jews who describe themselves as 'secular' or 'not religious' fast on Yom Kippur and 24 percent of them have attended prayers at a synagogue."
As for me: I'm aware today that it's Yom Kippur. I am not doing anything that I wouldn't do anyway. I neither purposely violate the spirit of the holiday nor do I do anything to uphold it. There have been years when I wasn't even aware of the holiday, and years when I was invited to "break the fast" dinners which I attended even though I wasn't fasting. I maintain a neutral attitude, I guess. You?