The problem will occur if judges are not able to insulate the tribunal against that influence. If they are unable to do that, then there are going to be serious questions about the tribunal's fairness and credibility.
This could have a chilling effect on the willingness of competent lawyers to vigorously defend the accused and that could have a fatal effect on the fairness and effectiveness of the trial.
In the face of provocative outbursts, the judge has to be firm but not trigger-happy in applying sanctions if fairness is going to be respected.