Is Ireland spelt Australia? To my mind unless posted in "Electrics Outside of the UK" we are working on UK rules, yes Ulster, Scotland, Wales, and England do have slightly different rules, but be it Ulster and the Republic (until Brexit) or Wales and England it is often only the council tax bill that tells one which country/principality one is in. The Pub with one bar in England and one bar in Wales has now closed, but the boarder specially in the Marches does follow a odd path, so for me in Mid Wales to visit my son in North Wales I cross the boarder many times. And the same applied around Derry or London Derry in Ireland.
When I worked in Ulster one would see the paving stones marked with three colours and this changed without crossing the boarder, so showing the republican flag does not mean they are not in Ulster, and to comment on the flag shown is a political act, or religious, so I would say we should ignore the flag and assume if posted in this section it is British.