We study an agent-based opinion model with two extreme (opposite) opinion states and a neutral intermediate one. We adjust the relative degree of conviction between extremists and neutrals through a dimensionless parameter called the “neutrality parameter” to investigate its impact on the outcome of the system. In our model, agents move randomly on a plane with periodic boundary conditions and interact with each other only when they are within a fixed distance threshold. We examine different movement mechanisms and their interplay with the neutrality parameter. Our results show that in general, mobility promotes the global consensus, especially for extreme opinions. However, it takes significantly less time to reach a consensus on the neutral opinion.