That's where their markets are. That's where millions of their citizens live.
The value to Ireland of the EU was to deliver union with Great Britain without having to be united with Great Britain.
Now, if GB leaves the EU (which I do not believe for a minute will be allowed), 95% of the value of the EU to Ireland will be gone.
Since both countries (the UK and Ireland) are controlled by atheists, and since most of the population of both islands is effectively anti-Christian, there really is no reason for them not to unite.
The UK intends for Ireland to remain in the Common Travel Area after Brexit, so Irish people can continue to live and work in the UK with no issues. (As I understand it.)