reland was an island
Ireland has long been a relatively unified entity with links to what is now Western Scotland. Due to its size and relative homogeneity it can't easily be compared with Poland in the middle ages.
In Ireland they were building monasteries, producing beautiful illuminated manuscripts and creating a literary history of their people when the ancestors of today's Poles were barely standing upright and living in a swamp.
waves of migration
Migration yes, however it was still remarkably homogenous. It is not a huge island and the population is small.
There was a Norman French ruling class who eventually assimilated, and settlers from England in County Wexford who spoke a language called Yola (an Anglic language related to Middle English) until the nineteenth century. The English language caught on relatively late: the medieval ruling class didn't much use it and any settlers from England or Scotland were relatively few and localised apart from the Ulster Scots in the North who have their own traditions and are all too assertive about that.
There's migration now, especially from Poland. It's too early to say what changes that will bring, however Ireland is not in any sense a melting pot. The south is very rural and Belfast is post-industrial.
The current situation with customs borders and the EU is about balancing the needs, Anglic and rights of the different communities there. It isn't Donbas.
The protestants in the North rightly object to a hard border with the rest of the EU and silliness like paying tax on parcels and the catholics rightly want seamless access to the south. Hence a workable solution being sought.
If we've learnt one thing in our long shared history, it's that we both like common sense and prefer peace to acrimony.
As I say, we aren't France or r*ssia.