Warning: Contains SPOILERS for The Book of Boba Fett episode 5.
Din Djarin (Pedro Pascal) is no longer a Mandalorian after The Book of Boba Fett episode 5, and yet he still retains the right to wield the Darksaber - here's why. The Book of Boba Fett episode 5, "Return of the Mandalorian," delivered on its titular promise with the appearance of Din Djarin, and yet also surprisingly flipped it too. Din wasn't the only Mandalorian to return, as he appeared alongside the Armorer (Emily Swallow) and Paz Vizsla (voiced by Jon Favreau, with Tait Fletcher in the suit), but more importantly he wasn't a true Mandalorian by the episode's end, banished after it was revealed he'd previously removed his helmet in front of others.
In a sense, Din leaving the Mandalorians - or more specifically, the Children of the Watch - behind has been on the cards for some time, since he's learned across The Mandalorian that the Way of the Mandalore is not the only way to live. But it coming via him being exiled, rather than a choice, makes it more surprising, but what really adds to that - and to the irony with it - is that Din had just proved himself beyond doubt as the rightful owner of the Darksaber by besting Vizsla in combat.
Interestingly, Din keeps the Darksaber after being stripped of his standing as a Mandalorian, raising further questions about the weapon's rules and place in Mandalorian society. While there would be a certain logic in the Darksaber only being rightfully wielded by an actual Mandalorian, and so one might've expected the Armorer to prevent him from keeping it, there's no firm rule to suggest that's actually the case. The Darksaber's Star Wars history is long and bloody but, as The Book of Boba Fett episode 5 makes clear, it can only be truly won in combat; Din Djarin did that against Moff Gideon (Giancarlo Esposito), and he did so again versus Paz Vizsla. Even if he's not a Mandalorian, there's no doubt that he has won the blade fairly, and not even the Armorer could deny him that without contradicting the Mandalorian Code herself.
There is strong precedent in Star Wars canon for a non-Mandalorian wielding the Darksaber too. Of course, Moff Gideon himself took it from Bo-Katan Kryze (Katee Sackhoff), and while she understandably wanted to reclaim it and enact revenge on Gideon for his atrocities against Mandalore, it didn't seem in question that the Darksaber belonged to him. Similarly, during Star Wars: The Clone Wars, none other than Maul (Sam Witwer) claimed the Darksaber by defeating Pre Vizsla (a relative of Paz) and became leader of the Death Watch, recognized as the Darksaber's true owner despite not being a Mandalorian. Conversely, Bo-Katan, while undoubtedly a Mandalorian, was never the rightful owner of the Darksaber since she didn't win it in combat. Therefore, while Din may not be a Mandalorian anymore (for now, at least), his claim to the Darksaber can't be revoked without him being defeated in combat.
Another question raised by Din's expulsion from the Mandalorians is why the Armorer allows him to keep his helmet and armor, which is pure beskar and, unlike the Darksaber, does by right (as they define them) belong to the Mandalorians. This is established by Din's beskar spear being melted down to make what appears to be armor for Grogu in The Book of Boba Fett episode 5, but also by Din's reaction to Boba Fett's armor in The Mandalorian season 2, where he takes the suit from Cobb Vanth, and later tells Fett that, "beskar belongs to the Mandalorians."
Since Din is no longer a Mandalorian, then his armor no longer belongs to him; however, the Armorer may be giving him something of a brief pass, given it's likely Din will head to Mandalore and try to atone (and, of course, Disney isn't going to rob the Mandalorian of the iconography). The Mandalorian season 3 should be able to draw these threads together, with Din once more becoming a true Mandalorian and further proving himself the rightful owner of the Darksaber, uniting what's left of the Mandalorians behind him.
The Book of Boba Fett episode 6 releases Wednesday 2 February at midnight PST on Disney+.