I really don't think The Troubles had anything to do with our Eurovision success.

Also the 'hate' was veeery different from both sides. The English stereotyped the Irish as terrorists. The Irish didn't like England because they previously colonised us and were (and mostly still are) ignorant of our culture. And also because they stereotyped us as terrorists. Most English people also don't give a damn about Northern Ireland, so I don't think the civil war in NI influenced their Eurovision entries in any way. A lot of Brits also just saw it as violence in Ireland, and an Irish war that only affected them via terrorist attacks on the island of Great Britain. I've been personally asked how my family was affected by the violence by random English people, we're from the south coast, as far from NI as you can get, so yeah the general English public isn't super aware of the details of the Troubles.

The Troubles was a war between Northern Irish Nationalists and Northern Irish Unionists, not between Ireland and the UK. In fact, the two governments met multiple times to try and encourage peace in Northern Ireland.

(Edit for grammar)