Lots of first-world countries have Internet. Not a lot of first-world countries have the amount of shootings, including mass shootings, the US has. That makes me doubt that the Internet is the problem.
The older Brits voted for the Brexit in mass, and they're much less likely to get their information from Social Media than the younger generations who voted to stay in mass. Also the British papers and television were largely in the stay camp as well
Add to this reactionary forces, whereby groups step up their rhetoric in defence against a perceived threat to their worldview, and you see that part of what spurred the non SM older brexit group was opposition to theincreasingly shrill and derogatory warnings from the remainers.
Essentially, I think social media catalyses division, regardless of whether you directly consume it or not.