Here's an answer to a very similar question that I wrote several months ago:

When people talk about things Celtic, they're usually conflating a material culture and language family into one cultural package. In reality, Celtic speakers were not required to use the associated material culture, like in Iberia, while the material culture could be used by non-Celtic speakers, which was the case in a large part of Central Europe.

It's still a contentious issue but I don't think that many Celticists would use the term 'Celtic' or 'Celt' without some sort of qualification. I'd say that there is still a use for the term, but it should only really be applied to speakers of a Celtic language regardless of their political or cultural status. Think of it like the term 'Germanic' - you could use it to refer to speakers of Danish, Old Norse, Crimean Gothic, Frankish or African-American Vernacular English, but it has no political or cultural associations beyond that.

There's actually an interesting dynamic in the Celticist world of academia: there are many people in Ireland, Wales, Brittany and Scotland who unreservedly stand by the pan-Celtic identity. Of course it's a completely modern identity with no basis in the historical past, but it's in some ways integral to how these people conceive of themselves as Irish, Welsh, Scottish etc. The contention arises when these kinds of people interact with Celticists, because they naturally take an interest in 'Celtic' history.

As I've said, most Celticists have done away with the unifying Celtic concept, and often clash with modern day self-identifying Celts who peek their heads in to glean some historical basis for their identity, only to find that the scholars committed to its study deny its existence. It's a really interesting phenomenon where the study of history/archaeology intersects with/comes into conflict with contemporary issues of identity, but in a context that isn't very racialized or colonial - these are often scholars of British or Irish heritage interacting with other people of Irish or British extraction.

And another:

The connections shared between Celtic speaking peoples are very superficial once you actually compare the details of different 'Celtic' societies. For example, both early Ireland and pre-Roman Gaul were societies with druids, a warrior aristocracy, a class of men of arts and a substantial peasantry dependent on that aristocracy. However once we look at the details the two are almost incomparable: the Gallic aristocracy's relationship to its peasantry was a direct and coercive one based on the ownership of land in the context of a monetary economy while in Ireland the aristocracy only had recourse to indirect means of control through client-patron relationships based on contractual cattle-lending.

The Gallic economy was one based on sedentary agriculture and substantial interaction with the Mediterranean monetary economy, while the Irish economy was overwhelmingly based on pastoralism, and coinage wasn't produced there until the 11th century. Gallic polities appear to have been early states, with republics and kingdoms, while Irish polities can be labelled as complex chiefdoms until about the 13th century. As well, the Irish warrior-aristocracy only really developed to become a central player in politics and society around the 4-5th century, centuries after Gallic civilization had died out. Gallic druids appear to have served as priestly magistrates and diplomats, while it's been theorized that Irish druids were central political actors before the supremacy of the warrior aristocracy.

I'd argue that Balkanizing the Celts is necessary if you want to study one of those societies on its own terms.

To give an answer to this question, I'll quote one of my favorite bits of Caesar's Gallic wars, describing the island of Britain (V.12-14). While Caesar was, of course, very much an outsider to the subject, he was also intellectually curious and worked closely with several Gallic leaders, and so what he says can be taken as a good reflection of attitudes among at least a subject of the Celtic speaking peoples:

The interior portion of Britain is inhabited by those of whom they say that it is handed down by tradition that they were born in the island itself: the maritime portion by those who had passed over from the country of the Belgae for the purpose of plunder and making war; almost all of whom are called by the names of those states from which being sprung they went thither, and having waged war, continued there and began to cultivate the lands...The most civilized of all these nations are they who inhabit Kent, which is entirely a maritime district, nor do they differ much from the Gallic customs. Most of the inland inhabitants do not sow corn, but live on milk and flesh, and are clad with skins.

The entire region was at this time inhabited by Celtic speakers, but you can see that these people themselves saw an ethnic distinction between the people of Gaul/Maritime Britain and the people of the interior of Britain. In fact, it seems from here that the "civilized" Gauls viewed the Britons in a similar way that the Romans viewed the Gauls.

Now a wrinkle is that one hundred fifty years later Tacitus' "Agricola" admits no such distinction. The obvious explanation, of course, is that Tacitus was simply less knowledgeable or less interested in conditions in the region, but the interesting explanation is that one hundred and fifty years of being on the business end of Roman imperialism had forged a common identity.