If an officemate wanted to be a free rider on one of those they could, and it would be very unlikely any harm would come from it.
If we had a 90% vaccination rate for this coronavirus we would not be having this conversation (and several hundred Americans would not be dying daily from a preventable illness).
As for the flu, its not especially dangerous, not prone to exponential spread, pre-symptomatic transmission is rare and the vaccines are not especially effective. So the flu shot is in a different class than the others.