Is not A United Ireland is more important than an anthem?

The thing is, I don't think that changing the anthem would do anything to bring a united Ireland nearer. In fact I can quite imagine ways in which it could be even more divisive.

Symbols like that are complicated things. The fact that the RUC had shamrocks on their badges never helped convince Nationalists and Republicans that they was on their side. If anything it was seen as adding insult to injury.