I wouldn't say it was all down to the referendum in that a similar divide has opened up in the US, for example, around Trump. I think the ubiquity of social media and people being able to choose news outlets which feed their particular world view have been massive influences on the divisions which have emerged. Once you've arrived a view on any issue you will find an enormous amount of info to confirm your belief and you can choose not to see any which might question your view. Previously, you had pretty much consistent output across TV and radio, although the choice in printed media was more varied.