Following Axelrod’s model of cultural dissemination (Axelrod, 1997), formal computational studies of cultural influence have suggested that the larger geographical range of communication in a globalizing world – in particular due to the rise of the internet - may increase global cultural homogeneity and decrease polarization. However, more recent extensions of Axelrod’s model (e.g. Greig, 2002) point to the possibility that global interaction may also sustain diversity by allowing local minorities to find outside support against pressures to conform to local majorities. In the present paper, I argue that these studies may not have gone far enough. I show that two relatively small but consequential extensions of Axelrod’s social influence mechanism turn the effect of range of communication upside-down. The first extension is to assume a continuous opinion space and thus align Axelrod’s model with previous studies of social influence (French, Harary, Abelson, Friedkin). The second is to add rejection and heterophobia to the model. In short, w hen perceived cultural differences between two agents are too large, they are assumed to reject each others’ opinions and develop an increasingly hostile relationship. Computational analyses of the model based on Hopfield’s attractor neural network demonstrate that now increasingly global communication increases rather than decreases the extent of polarization in the population, contrary to Axelrod’s original conclusion. Further experiments identify the window of conditions under which the effect obtains, including a relatively small number of cultural features, and – counterintuitively – a relatively high degree of moderation, that is: willingness to accept small cultural differences.