Unprecedented possibilities of quadruped robots have driven much research on the technical aspects of these robots. However, the social perception and acceptability of quadruped robots so far remain poorly understood. This work investigates whether the way we design quadruped robots' behaviors can affect people's perception of safety in interactions with these robots. We designed and tested a dominant and submissive personality for the quadruped robot (Boston Dynamics Spot). These were tested in two different walking scenarios (head-on and crossing interactions) in a 2x2 within-subjects study. We collected both behavioral data and subjective reports on participants' perception of the interaction. The results highlight that participants perceived the submissive robot as safer compared to the dominant one. The behavioral dynamics of interactions did not change depending on the robot's appearance. Participants' previous in-person experience with the robot was associated with lower subjective safety ratings but did not correlate with the interaction dynamics. Our findings have implications for the design of quadruped robots and contribute to the body of knowledge on the social perception of non-humanoid robots. We call for a stronger standing of felt experiences in human-robot interaction research.