OK, Iowa Corn... let's think this through. You have two options. (1) Stick with the current design of the trophy; or (2) Change the design to something more palatable to both fan bases.
Upside under scenario (1): You don't have to admit that you messed up and you don't have to incur any additional expense in a re-design. Perhaps you don't have to hurt the feelings of the CEO's wife/daughter who design this trophy (that the CEO's wife/daughter designed this is the only possible conclusion that can be drawn).
Downside under scenario (1): You have two entire fan bases that hate your organization and desire to kick Captain Corn straight in the cornhole. The players are too ashamed to hoist the trophy after victory and perhaps leave it "accidentally" at the other team's stadium after road victories. Further, you appear stubborn and concerned more about some politically-correct statement than the fanbase. Essentially, everybody sees the trophy for what it is--a celebration of your organization and not the fan bases, the schools, or the games. People come to view you with contempt, when they otherwise would have viewed you with indifference or benevolence.
Upside under scenario (2): You have second chance to create a trophy that the fan bases and players deem worthy of hoisting after victory. You avoid all of the ill-will that is described in the downside to scenario (1).
Downside under scenario (2): Additional expense and you have to admit you messed up (and maybe hurt some feelings).
This really is not a difficult decision.
Here, let me draft the press release for you.
On Friday, August 19, Iowa Corn unveiled to the general public a new design for the Cy-Hawk Trophy, the trophy awarded to the victor of the annual football game between the University of Iowa and Iowa State University, to replace the original design of the Cy-Hawk Trophy which had been in use since [insert date of year of first use]. Although much thought, time, and effort went into the original re-design of the Cy-Hawk Trophy, as a result of concerns expressed by the fan bases of both universities we have decided to abandon the original re-design and create a contest open to the general public for a new design for the Cy-Hawk Trophy. It was a very difficult decision to abandon the original re-design, because we believe that it embodied the best of the State of Iowa--dedication to family and the State's leading industry, agriculture. However, because we recognize the annual Cy-Hawk football game is a celebration of the the universities, the players, and the fan bases, we have decided to allow the fans to submit their own ideas for the Cy-Hawk Trophy. Iowa Corn will select the top ten proposals submitted by fans and post them on our website at [insert page address]. All fans will then have an opportunity to view the various proposals on our website and vote for their favorite. Iowa Corn is proud to sponsor this excellent football rivalry and is excited to present this opportunity to the fans.