I think it's not so much the referendum itself, as that the referendum has revealed some uncomfortable truths about the views of the people we are close to- whichever 'side' you fall on.
I voted Remain. My entire family (apart from DH) voted Leave. My Mum was upset yesterday that there's been so much aggression on social media towards Leave voters (not, I hasten to add, from me). I pointed out that people feel strongly, they are scared, Remain voters are just as passionate about the issues at hand as she is. I have avoided seeing my parents today because I do need time to calm down. I don't want to hurt my Mum. I'll see them tomorrow and smile benignly and say "I hope you're right" if they bring up the Referendum.
The only person I have engaged with is a friend's DH who shared a hateful meme last night calling Remain voters pathetic. I told him that I respected his right to vote as he saw fit, which was why I hadn't challenged his views before, but that the meme was divisive, unhelpful, unkind. That his friends were scared and he was mocking their fears, which is a pretty low thing to do, regardless of whether he agrees with them or not. That we needed to heal the rifts that the referendum has revealed, and that the 'winners' could be sharing positive messages to help this, if they need to share anything at all.
He replied- "lol". So I will be avoiding him for some time- as I would've avoided a Remain supporter who crowed over Leave voters if the result had gone the other way.