The curious case of Mandy Moore gives us some insight:
Mandy’s maternal grandmother was an English war bride, who also had some Irish ancestry. Mandy’s maternal grandfather was a Jewish American soldier, of Russian Jewish and Galician Jewish descent.
Once you start mixing, you just go further into the process. Irish people are part Mediterranean, as are Jews, so the mixed parts recognize each other. Their offspring then present as one side or the other, and marry in that direction. This can however change over the generations:
She is married to singer, songwriter, and guitarist Taylor Goldsmith.
She clearly favored the Irish/Jewish side, and selected a husband to match.