Opinion dynamics in relative agreement models seen as an extension of bounded confidence ones, involve a new agents’ variable usually called opinion uncertainty and have higher level of complexity than that of bounded confidence models. After revising the meaning of the opinion uncertainty variable we conclude that it has to be interpreted as the agent’s opinion toleration, that changes the type of the variable from the social to the psychological one. Since the convergence rates to the stationary states in dynamics of sociological and psychological variables are in general different, we study the effect of agents’ psychology and social environment interaction on the opinion dynamics, using concord and partial antagonism relative agreement model in small-world and scale-free societies. The model considers agents of two psychological types, concord and partial antagonism, that differs it from other relative agreement models. The analysis of opinion dynamics in particular scenarios was used in this work. Simulation results show the importance of this approach, in particular, the effect of small variations in initial conditions on the final state. We found significant mutual influence of opinion and toleration resulting in a variety of statistically stationary states such as quasi consensus, polarization and fragmentation of society into opinion and toleration groups of different configurations. Consensus was found to be rather rare state in a wide range of model parameters, especially in scale-free societies. The model demonstrates different opinion and toleration dynamics in small-world and scale-free societies.