Unfortunately, the Lara Cassidy paper on Ireland's genetic history is now embargoed. But it will interesting to read that paper with this linguistic question in mind:
"why are there typological similarities between Insular Celtic and Afro-Asiatic?"
Cassidy at Eurogenes. Hopefully someone will send me the PDF, but until then, the question...
The mainstream view is that the Celtic entered the Islands in the LBA with the IA representing its cultural apex. Population movements certainly spread this language, but genetic continuity would suggest that Bronze Age natives would have learned Celtic (as a new dialect or a new language)
Before the Celtic invasion, the Island of Britain probably spoke a number of languages related to those of the Low Countries (certainly some kind of LLPIE, possibly the speculative Nordwestblok). But Ireland may be another story as its ethnic enclaves were more choppy, with strange menages of new lifeways and ancient craft traditions. (food vessels as one example)
We think of the modern Irish as supremely North European with high frequencies of new traits associated with Bronze Age population movements. But we must remember that this was a long and cruel process on a little Island. A little Island that spent a lot of energy harassing and conquering the West Coast of the big Island. We have to be careful looking at Bronze Age Ireland though our modern prism of Celticity.
If Late Neolithic Irish tended toward the more Levantine variety of Farmer, and if they survived in any significant numbers to the MBA in Ireland, then it is well possible that portions of the LBA Irish population were learning (or mangling) Continental Celtic from the aspect of an Afro-Asiatic thinker.
I'll offer a speculative possibility for consideration...
1. Western European farmers descend from two major ancestral epochs/bodies
a. Danubian farmers originating in Anatolia and SE Europe that were variously mixed with Hunter-Gatherers (these are the I2 and G guys and are the majority throughout the continental heartland)
b. Maritime farmers originating in Syria that dot the littorals and river valleys across North Africa, parts of the Northern Mediterranean, and parts of the Atlantic facade to Ireland (these are possibly the carries of R1b-V88 and E1b among others)
2. Although Bell Beakers (probably IE speakers) pummeled most of the large Island, the Irish Sea and Ireland itself may have been more patchy in settlement where Neolithic cultural ways and ethnicities lingered and inter-married through the Early Bronze Age to Middle Bronze Age.
3. The bastard Celtic of the Irish Sea and Southern Ireland came to dominate or influence all of the Islands throughout the Iron Age, so what happened on the macro level doesn't matter anyway.
4. Insular Celtic was spread by Irish Bastards with daggers and swords.
See also: Insular Celtic Languages
**Update**
See also: Dispatches comments
CASSIDY, LARA, A Genomic Compendium of an Island: Documenting Continuity and Change across Irish Human Prehistory, Trinity College Dublin.School of Genetics & Microbiology. GENETICS, 2018