Karlstadt was an iconoclast. Of course he didn't like crucifixes. He didn't like statues of Jesus, either, so he would have been appalled by the Christus statue in SLC.Early and traditional Christian figures such as Martin Luther’s associate Andreas Karlstadt (1486–1541) were arguing by the late Middle Ages that “the crucifix [on its own] depicted only Christ’s human suffering and neglected to display his resurrection and redemptive [powers]” (in John Hilton III, Considering the Cross: How Calvary Connects Us with Christ [2021], 17).
Also, while it's technically true that he was an associate and early supporter of Martin Luther, they soon had a bitter falling out and Luther denounced him.