The classic influence maximization problem finds a limited number of influential seed users in a social network such that the expected number of influenced users in the network, following an influence cascade model, is maximized. The problem has been studied in different settings, with further generalization of the graph structure, e.g., edge weights and polarities, target user categories, etc. In this paper, we introduce a unique influence diffusion scenario involving a population that split into two distinct groups, with opposing views. We aim at finding the top-$k$ influential seed nodes so to simultaneously maximize the adoption of two distinct, antithetical opinions in the two groups, respectively. Efficiently finding such influential users is essential in a wide range of applications such as increasing voter engagement and turnout, steering public debates and discussions on societal issues with contentious opinions. We formulate this novel problem with the voter model to simulate opinion diffusion and dynamics, and then design a linear-time and exact algorithm COSiNeMax, while also investigating the long-term opinion characteristics in the network. Our experiments with several real-world datasets demonstrate the effectiveness and efficiency of the proposed algorithm, compared to various baselines.