If you look at the last couple of thousand years of history, the world has slowly but surely become more liberal. There have been large backward steps—such as the rise as fascism in the 30's and the recent increase of Islamic fundamentalism—but it seems to me it's always been one step back and two steps forward. In the end, regressive movements always lose and society gradually moves forward to a more liberal position: the emancipation of women, votes for the working classes, votes for women, free movement of people and trade, universal human rights, education for women and girls, the end of slavery, same-sex marriage, gay rights etc.
Brexit, Donald Trump, the rise of the 'alt-right' and their so-called 'culture war', the demonisation of immigrants and refugees, the anti-vax movement, the hatred of intellectuals and academics...are tiny blips in history, which will inevitably be swept away by societal evolution.
As an example, look at today's teenagers and twenty-somethings and compare their values to mine, a child of the 70's and 80's. We were openly racist and homophobic, as were many of the adults. That kind of behaviour would be abhorrent to most kids these days, who are much more accepting of different cultures, sexualities and races. Give it thirty years and the current crop of illiberal voters who seem hell-bent on restricting our freedoms will all be dead and buried. Swept away by history, along with their beliefs.
Leave voters are political and intellectual dinosaurs, sitting happily by their watering holes, with no idea they're about to become extinct.