"In a country where every other sport is happily played on an all-Ireland basis, why does football suffer the indignity of such tension?"
This is simply wrong. Consider those other sports:
Rugby Union: the supposedly all-Ireland side plays almost* all its matches in Dublin, and runs out only to the South's national anthem under only the South's national flag. Its one full international in NI in the last 50 years was treated by the IRFU as an away fixture. Happily all-Ireland my hole.
GAA: the Association has discriminated aganst the British and Unionist communities in Ireland for decades, barring large groups from membership, 'foreign' games from using facilities and continuing (in 2012)to commemorate convicted paramilitaries in its competitions, club names etc. Happily all-Ireland my hole.
Athletics, other Olympic sports etc.: although the South's Olympic bodies claim jurisdiction over all-Ireland (and are quite happy to enrol NI competitors when their own aren't good enough), in practice those competitors have a choice who they declare for. Indeed many have turned out for both the South in the Olympics and NI in Commonwealth Games etc. That doesn't stop Dublin's Olympic mafia throwing Hickey fits when their British equivalents sign up NI competitors. Fcuk em, happily all-Ireland pretty much my hole.
Loser citizenship rules since 1998? Not really. NI footballers were eligible for the South well before that, but tended not to play for a combination of reasons- the South were weaker, IFA pulled rank and it just wasn't a political issue.
The Irish Republic's citizenship rules have clearly got tigher recently, most obviously in 2004 when a referendum supported by 80% confirmed that birth on the island would no longer confirm it automatically.
Do better.