I think it is heart- breaking that so many on the left seem to think that it is 1) acceptable and 2) effective to insult and denigrate anyone who disagrees with them.
I don't see that's what's heart-breaking at all. For me, it doesn't even enter the top...5 about what's so tragic about where we are as a country right now. I agree with you its a mess. 
For me, successive politicians have tried to scapegoat immigrants and the EU as responsible for many of the woes of people's lives. It's served a purpose - but I don't believe that's true. The facts don't support it either. That makes me really sad.
I think Cameron called the referendum to unify the party and we all got dragged in - and he foolishly failed to understand the ground-swell of opinion against EU and immigration. That makes me angry.
I believe leaving the EU will be shit for most of us and catastrophic for some businesses and communities. That makes me v. sad.
I hate the fact that my EU friends are feeling so insecure - because of this vote.
I hate the fact that our jobs are not strong or stable - because of this vote.
When you ask some leavers (not all) for their reasons, they don't add up in any way - they are based on lies and mis-information. (and racism) I'm sorry if that's unpalatable, but this has been my experience in RL. I live in a big leave area. That makes me sad.
On Mumsnet, my experience has been, most leavers, (with an exception of say, two I could name off my head) don't seem able to engage in political or economic debate - 'we've done all that' but prefer to divert any discussion away from 'issues' to the old 'we are not ALL racist or thick'.
Actually, that one is not heart-breaking
that's just annoying.