Hamilton County Judge Leslie Ghiz ruled that the shirt, which displayed a confederate flag, has no bearing on the case.
Judge Ghiz also ruled that experts for both the defense and prosecution will be allowed to testify about the body cam video.
Jury selection in the case started Thursday. The pool of 243 potential jurors was whittled down to 180. The selection process will resume on Tuesday.
Tensing is charged with murder and voluntary manslaughter in the fatal shooting of DuBose, which happened during a July 2015 traffic stop.