but have always been shouted down and their feelings treated with ridicule
The additional use of inappropriate language doesn't help serious conversation,
It's a question of perception though, isn't it, Jabberwock? Leavers see things completely differently from Remainers. Leavers give their reasons for their vote, Remainers give a counter argument or point out that something is not true and get accused of 'shouting down'.
As for 'inappropriate language;, despite what POGS asserts, but declines to give evidence of, I haven't noticed the use of the sort of 'robust' language that characterises, say, a mumsnet discussion.
Or is serious conversation meant to be agreement over everything?
As I said, our perspectives are completely different.