You’re correct that this issue is important in the primary, and I hope the ad will cause Rep. Ives to gain support.
I disagree about your definition of “closed primary.” I have a B.A. in political science. In one of my classes, I learned that there are three main types of primaries, closed, open, and wide open. If a state has closed primaries, each voter must choose a party, when he or she registers to vote. During the primary, a voter may only receive a ballot from that party. Usually, those states prevent a voter from changing his or her party fewer than 30 days before the primary. If a state has open primaries, the voters don’t choose a party, when they register. During the primary, each voter may choose a republican or democrat ballot. If a state has wide-open primaries (including California, Washington, and Michigan), all primary voters receive a large ballot that includes candidates from all parties. According to the above definitions, Illinois has open primaries.
In Illinois, voters must declare their party preference to receive a ballot.