As already explained there is almost no chance for a solely Irish citizen becoming an RAF pilot through the normal methods. In fact the big issue is security clearances. Certain roles are out of bounds because it isn't possible to obtain a full security clearance. Even the army which is happy to take Irish citizens has some jobs which are not available.
If Ireland had joined NATO, I doubt there'd be a problem.
However there is no bar to enlisting in the RAF as an airman. I'ts possible after a couple of years a certain flexibility will be shown. Bit of a gamble though.
Ironically if you were born in Northern Ireland, there is no problem even though that's were all the troublemakers come from!