We introduce a minimal opinion formation model that is quite flexible and can reproduce a wide variety of the existing micro-influence assumptions and models. The model can be easily calibrated on real data, upon which it imposes only a few requirements. From this perspective, our model can be considered as a bridge, connecting theoretical studies on opinion formation models and empirical research on social dynamics. We investigate the model analytically by using mean-field approximation and numerically via Monte Carlo simulations. Our analysis is exemplified by recently reported empirical data drawn from an online social network. We demonstrate that the model calibrated on these data may reproduce fragmented and polarizing social systems. Furthermore, we manage to generate an artificial society that features properties quantitatively and qualitatively similar to those observed empirically at the macro scale. This ability became possible after we had advanced the model with two important communication features: selectivity and personalization algorithms.