I'm not sure about that since to the best of my knowledge, almost every international sport features a single All-Ireland team except for football.......Maybe before the Good Friday Agreement had marked the weakening of the overt politico-religious conflict in Ireland I could see where this might be a factor, but not so much today....
Nope, thats not true at all. Only Two days ago a move was made by several Unionist boxing clubs in Belfast to petition a change in the law that allows separate competition for Northern Ireland away from a United Ireland, as (and this is acknowledged by both sides) Unionist fighters from Protestant suburbs of Belfast who want to fight under the banner of a British Flag and sing their own official national anthem, have instead to listen to Londonderry Air and fight in the colours of Ireland. This also creates huge problems under the radar at local level when, as Northern Irish Protestant also end up having to fight in Ireland or forced to fight in Catholic dominated areas, they are increasingly becoming subjected to racial, religious and physical abuse, threats, etc.
In fact, the captain of the N. Irish boxing team stated after winning gold in the Commonwealth games (where Ireland are split) he did not acknowledge the medal ceremony as it "wasn't his flag, and wasn't his anthem" (or words to that effect). He wasn't the only one, and on both sides of the catholic/protestant divide. Boxing is a very good example as Northern Ireland has a vibrant and increasingly popular/successful working class following that is producing talent all over the place, and is not like rugby, an old established sport where a United Ireland team was created before the Irish Free State was created, and where it is limited to a small percentage of upper or middle class people, who are generally accepted to have been far less entrenched by sectarianism. It is clear in Boxing that the issues are becoming more prevalent, and that many boxers want the right to box under the colours, flag and nationality that they are. Interestingly, it is the Catholic Sinn Fein Sports minister who is resistive to a change and refused to grant ..... maybe because she prefers due to her political affiliation, to have British Protestants fight in Gold, white and Green and forced to acknowledge they are Irish!!! In Football, another very popular working class sport, a United Ireland team would never have been accepted or was possible.
Rugby has its problems too, and there have been accusations for years that Ulster protestant players are overlooked on performance. The anthem and flag issue is also a problem here, and the cultural bias is not hard to identify.... The Irish team play in Dublin exclusively, which fly's a Tricolour along side a mongrel flag, which plays the Irish national anthem alongside a shared one..... but when in 2011, a game scheduled in Belfast for a WC warm up was supposed to be held, the Irish Board refused to ever consider using Northern Ireland as a venue again for the future when it was pointed out a Union Flag and God Save the Queen would be sung instead of the Irish NA, as the established precedent was to use the home venue alongside the United Ireland flag/anthem.
In fact, ever seen how many Irish players (Republicans) sing the Ireland's call???? It was noted in the WC it was first used, 27 of the 30 man squad refused to sing it. Even now, hardly any non-Republic born Irishman acknowledges it, as do the Northern Ireland players with the Republic anthem.
And if it still doesn't matter, check out how desperately political correct Rory McIlroy is when taking about which nation he will represent at the Olympics next year.