You'd think the writers at the University of Chicago student newspaper would know that.
Apparently attempting to reveal the president of the university as some kind of secret Republican is more fun.
The primary election is an attempt by self-styled good government types of a century ago to shift some of the power to select candidates from party insiders to voters. Thus, voting in a primary election involves requesting a party-specific ballot. In Illinois, a voter declares by making such a request at the check-in desk. There is no such thing as a list of "registered" Republicans or Democrats, the way there is in other states. Party operatives of all parties (in principle, you could have a libertarian primary in Illinois) prefer the closed primary, as crossover voting is a way for hard-core voters of one party to frustrate candidates of another party.
That might well be what the university's president, Robert Zimmer, did. He's reported as having voted in the 2008 Democratic primary (recall, dear reader, that both Barack Obama and Hillary Clinton had roots in Illinois) and then in the 2016 Republican primary, where a crossover Democrat might want to help Donald Trump win on the theory that he would be easy to defeat, or a Never Trump Republican still had a choice.
The Maroon article is getting slagged in its comment section.