LARNE, Northern Ireland—As Northern Ireland’s unionists prepare to celebrate 100 years since the state’s creation cemented their place in the United Kingdom, post-Brexit trade barriers are triggering their deepest fears: being cut off from Britain and pushed towards a united Ireland. The British-run region remains deeply divided along sectarian lines, with Catholic nationalists aspiring to unification with Ireland while Protestant unionists seek to retain the status quo. Nearly 23 years after a 1998 peace deal ended three decades of confrontation between the Irish Republican Army, pro-British “loyalist” paramilitaries and the British military, it is customs declarations and phytosanitary certifications that are now the focus of unionist angst. From Friday, many British goods entering the smallest of the United Kingdom’s four nations will require customs checks and paperwork under Britain’s withdrawal deal with the European Union—which keeps Northern Ireland in the UK’s customs territory but also still aligned with the EU’s …