The story says this was in an "Illinois Republican Party mailer":

I may have gotten one of these mailers and thrown it away without looking at it. But today it is on page 3 of the Chicago Tribune with an article about candidate Kevin Morrison raging that depiction of him as a puppet with a drooping wrist is a homophobic slur.

So: (1) The ad gets huge free publicity; (2) Attention is called to a detail of the ad that most people who did see it probably didn't even notice; (3) People who see the story now have the impression that Morrison is gay, whether he is or not, and which they may never have thought before, and which they may not care about, but they also may get the impression he is a whiny nit-picker. (I don't know if he is publicly gay, I couldn't tell from the article.)

So I don't know what they thought they would gain from this uproar, but I doubt it will have a positive effect on Morrison's vote total.

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Democrat depicted as a puppet in GOP campaign ad says it's homophobic against him
by Gregory Pratt - October 12 2018

A Democrat seeking to unseat Republican Cook County Commissioner Tim Schneider is accusing the state GOP of mailing out a homophobic campaign mailer, though Republican officials say it’s only meant to call the challenger a political puppet.

The Illinois Republican Party denies that the mailer it sent opposing Democrat Kevin Morrison, who is challenging Schneider, is meant to be anything more than an illustration that Morrison is beholden to Illinois House Speaker Michael Madigan and Cook County Board President Toni Preckwinkle.

The mailer depicts an extra-large Madigan crouching next to a comparatively tiny Morrison who’s depicted as a puppet. The ad portrays Madigan animating the puppet version of Morrison who is midpose with what appears to be a limp wrist.

Morrison countered by sending out a campaign fundraising mailer accusing Schneider of sending out an attack ad “picturing me with a ‘limp wrist,’ a bigoted caricature of gay people.”

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http://www.chicagotribune.com/news/local/politics/ct-met-cook-county-candidate-calls-mailer-homophobic-20181012-story.html