With respect to any kind of theological impact, I don't see one but we must remember that politics and religion are not strange bedfellows. I consider one to be looking up, the other looking down and little about their structures are otherwise that different from each other. I tend to reject them both with equal repulsion. Any time one champions atheism yet doesn't apply the same zeal for dismissing politics a certain obliviousness in their character exists. They are one in the same and the notion of separating church and state has always baffled my sense of logic. In politics we have partisanship, in theology we have religion. The goals and methods are the same and employ the same meme for the ignorant masses to abide.

Vote for me and I'll set you free.

The Brexit does not invoke any sense of a religious theme in me. It's all politics with the Brits finally finding their trousers and a decent pair of hiking boots. After a quick boot up Juncker's shady side as a last say in the matter, I believe they will turn on their heels and find their autonomy again. Junckers, too stupid to realize that great men are the product of events and timing, will not take this opportunity to make himself great and instead remain his usual sniveling cretin opposing the Brits at every turn.

I think it's mainly the result of populist nationalism and xenophobia. Immigration has always been controversial in the UK, and free movement for EU citizens is a condition of membership. The Brits have never considered themselves Europeans (like the Japanese do not consider themselves Asians), so many have felt threatened by the presence of large numbers of people from Poland, the Balkans, etc. Of course, British nationalists conveniently forget that their Royal Family are all Germans, except for Prince Philip, who's Greek. In fact, the last truly English King was killed at the Battle of Hastings in 1066. Since then they've all been French, Welsh, Scottish, Dutch, and Germans.

BREXIT and the election of Donald Trump can be traced to similar factors. Britain has its own rust belt areas. Those driving the UK down the Euro path didn't have the time, inclination or talent to convince the general populace of the benefits, so it was easy for Euro-sceptics like Boris Johnson to push the BREXIT line.

I don't think religion had anything to do with BREXIT. I doubt whether Brits care enough about religion for it to be a useful tool for BREXIT or anti-BREXIT campaigners.