Wiki is always a dodgy source but did you even take any time to read what you posted?
" was an annual football competition contested between the United Kingdom's four national teams: England, Scotland, Wales, and Ireland (the last of whom competed as Northern Ireland starting from the late 1950s)."
Note the use of 'was' - past tense and it even adds the caveat that it was Northern Ireland up until the 1950's but then Ireland joined it and Ireland is not in the UK. You are jumping between football and rugby and it is difficult to understand what point you are trying to make. I am stating for a fact that Ireland is not a Home Nation. Are you actually disputing that?
Yes, so the original footballing home nations included all of Ireland since this is a football forum and the original point was about football.