How much of the Irish and Scottish today are a mix of Celtic and Viking?

We have had our historical narritive polluted by the overbearing importance of essentially an aristocracy of arms who took over the high points of the local culture.  what truly mattered were the first movers who established an  economy able to support the extended local population.

Those first movers were largely cattle men who could support large families.  Exactly this happened to the First Nations in North America.

Thus the Viking invasions failed to displace the local populations at all and only led to intermarriage.  The same thing has happened in North america.  Large settler populations has steadily absorbed first nations throughout the USA.

How much of the Irish and Scottish today are a mix of Celtic and Viking as opposed to more directly descended from the Celts who arrived much earlier in the late bronze-early iron age?

Quora. com

Revolutionary breakthroughs in ancient DNA research in the past 15 years or so have revealed that the peoples of Ireland and Scotland are predominantly descended from the Bronze Age settlers known as the Beaker Folk. Depending on which studies you rely on, from 80 to over 90 percent of our genetic makeup is of Bronze Age origin. The next biggest element (but less than ten percent) comes from the neolithic farmers who left us such wonders as Newgrange and Callanish, and a small trace of the blood of the original, post-Ice Age hunter-gatherers flows in our veins as well. But the imprint of the people who came in historic times—Norse (“vikings”), Anglo-Saxons, Normans, and the rest—is surprisingly light.

There is no “Celtic DNA,” however, and it is now generally agreed that the 19th century belief in an Iron Age Celtic invasion of Great Britain and Ireland was based on little more than wishful thinking. There is simply no evidence (DNA or archaeological) of the arrival of a significant wave of settlers in the last millennium BC who replaced the descendants of the Bell Beaker Folk: we are still here.

The term “Celts” has been applied to a variety of tribal peoples who lived in central and western Europe (and even further afield) prior to and coterminous with the Roman era. Some of these tribes spoke what were much later labeled Celtic languages and others did not. The La Tène/Hallstat culture has long been classed as “Celtic” but was largely unknown to many supposedly Celtic peoples (including those in Ireland and Scotland). Nowadays, there is an increasing tendency among scholars to use the term “Celtic” only in connection with the languages, and the idea of a “Celtic race” that came with a complete linguistic and cultural package has largely been abandoned.

Celtic languages did, however, arrive and take root in the islands of Great Britain (Brythonic) and Ireland (Goidelic) by no later than the last few centuries BC. How, why, and even exactly when this came to pass is not really known, and is a matter of considerable inquiry and debate among scholars.

You also asked about the Norse (who were much more than just “vikings,” i.e., seafaring bandits). Although the Norse contribution to the Scottish genome as a whole is fairly small (no more than a couple of percent), it is much more significant in parts of western Scotland, the Hebrides, Orkney, and Shetland. This is not surprising because these were areas extensively colonized by the Norse. The Norse imprint on the Irish gene pool is smaller, but many of us (including me) claim some Norse ancestry.

In sum: (a) the Irish and Scots are largely descended from Bronze Age settlers; (b) although our ancestors acquired Celtic languages perhaps 2,500 years ago, we have no “Celtic genes” (because there are none); and (c) the Irish, on average, have some Norse ancestry but the Scots have more, especially in the west and the isles.