We demonstrate a simple model of opinion diffusion where a local opinion leader acts as the initiator of public discussion. We show the possibility of driving a significant wedge between opinions of two groups that exhibit homophily even though individuals are highly conformist. In particular, we show that there exists an opinion gap between the group which the opinion leader belongs to (referred to as the residence community) and the other group; and this opinion gap is increasing in the relative size of the residence community. Using a unique dataset of national referenda in Switzerland from 2008 to 2012, we show that members of parliament (MPs) match referenda outcomes in their residence communities closer than they do in neighboring communities, and this wedge interacts significantly with the relative size of the residence community, thus aligning with our theoretical conjectures. We conclude that observed opinion gaps can actually be overrated to the extent that they are driven by structures that underlie the social web of different groups within the society.