Party registrations are public, and you can make a pretty accurate guess that someone who is registered to one party is likely to vote for that party, too.

I can imagine a situation where someone's boss doesn't like a certain party or politician, and they decide to take it out on their subordinates that they suspect will vote/have voted for them. Seeing a D or R next to an employee's name and that they voted could be enough evidence for them to face discrimination or threats not to vote.