Spatially-situated opinions that can be held with different degrees of conviction lead to spatio-temporal patterns such as clustering (homophily) and to polarization. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms: spatial relocation, and non-local interaction (``telephoning''). We find that a relatively small amount of mixing by telephoning breaks up polarization and hastens consensus, and the effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations.