The Last Kingdom generally isn't considered to be historically accurate. There's about three years worth of questions on AskHistorians. Most are unanswered, and the few that have attracted discussion tend to view the show as an erroneous (and possibly problematic) depiction of the medieval past. Many of the most popular tropes from the show replicate fantasies also popularized by the History Channel's Vikings series, and Ask Historians has a whole FAQ section on that.

I've watched a season or two of the show and enjoyed it as an adventure story that occasionally draws on images from the past. The basic premise, however—that Viking-Age England pitted Christian Anglo-Saxons against pagan Danes—is entirely unsubstantiated.

There's good reason to believe that Alfred accepted a subordinate position to the "Danish" rulers of Mercia in the 870s (based on coins he minted in London while it was under Danish rule), and his later claims in the 890s that he represented Anglo-Saxon England was basically a way to assert rulership over neighboring areas never before ruled by Wessex. Alfred's nephew Æthelwold, who seems to be a bit of a buffoon in the show, actually seems to have had more success unifying Northumbria and East Anglia, to the point where he held sway over Mercia and might have unified all of Anglo-Saxon England—had he not died in battle against his father's former kingdom of Wessex. In Ireland, Æthelwold was remembered as 'king of the Saxons of the North' in the Annals of Ulster. At any rate, I think these two characters exemplify how ethnicity and religion were messy and perhaps even irrelevant to many actors in the early Viking Age.

In contrast, personal relationships were extremely important, and I think the show does a decent job at showing how these might sometimes trump what we might today consider rational political concerns. But the identity politics of the modern world—categorizing people according to ethnicity or religion and then pursuing policies of genocide to create 'pure' national communities—are problems of the 20th century, not the 9th.