In today's world, understanding different viewpoints is key for societal cohesion and progress. Robots have the potential to provide aid in discussing tough topics like ethnicity and gender. However, comparably to humans, the appearance of a robot can trigger inherent prejudices. This study delves into the interplay between robot appearance and decision-making in ethical dilemmas. Employing a Furhat robot that can change faces in an instant, we looked at how robot appearance affects decision-making and the perception of the robot itself. Pairs of participants were invited to discuss a dilemma presented by a robot, covering sensitive topics of ethnicity or gender. The robot either adopted a first-person or third-person perspective and altered its appearance accordingly. Following the explanation, participants were encouraged to discuss their choice of action in the dilemma situation. We did not find significant influences of robot appearance or dilemma topic on perceived anthropomorphism, animacy, likeability, or intelligence of the robot, partly in line with previous research. However, several participants hearing the dilemma from a first-person perspective changed their opinion because of the robot's appearance. Future work can expand with different measures such as engagement, in order to shed light on the intricate dynamics of human-robot interaction, emphasizing the need for thoughtful consideration in designing robot appearances to promote unbiased engagement in discussions of societal significance