A new fan theory proposes a spine-tingling twist on the Star Wars sequel trilogy: Rather than pass away at the end of The Last Jedi, Luke was never actually alive to begin with. Instead, he died the night the Jedi temple was destroyed, prior to the events of The Force Awakens, probably at the hands of Ben Solo. The only surviving witness was R2-D2, and it was so traumatic that it blew his circuits, which is why he was out of order for most of The Force Awakens.
According to this theory, posted on Reddit, when Luke passed away, he didn't yet know how to become a proper Force ghost, and he was very conflicted, so his spirit drifted to Ahch-To, the place of the first Jedi temple. When Rey arrives at Ahch-To, she doesn't really see or interact with Luke but has visions of him. By the end of The Last Jedi, Luke has mastered his spirit form, and that's why he can project it across the Galaxy.
So, let's see if this theory might work in any way, shape or form, by referring strictly to the source material: The Last Jedi itself and its novelization.
The novelization opens with a prologue from Luke's point of view, where it is made abundantly clear that he was still alive, and that he wished his life had taken a different path.
In Ahch-To, and both in the movie and in the novelization, Luke interacts with Rey, Chewbacca, R2-D2 -- who is the closest in-universe character to an objective observer -- with the island caretakers and with Yoda. These last two interactions do not take place in front of Rey, which should disprove that she's hallucinating Luke's existence.
Luke is hesitant to run into a Jedi tree after Yoda strikes it with lighting, which is a very reasonable fear for someone with a vulnerable body. In the novelization, the last chapter is told from the point of view of the head caretaker of Ahch-To, and she notes that Luke was alive on the island, participating in the daily routines, and then one day he disappeared to become one with the Force.
From a narrative standpoint, Luke being literally dead doesn't work either. Metaphorically it is true that Luke suffered a "spiritual death" the night he almost killed Ben Solo in his sleep, only to lose the Jedi temple and every single one of his students, but his whole arc in The Last Jedi consists of him coming back from this self-imposed limbo to help the people he loves. Luke's inner journey and sacrifice would not make any sense if he were already dead to begin with.
Furthermore, the seeds for Luke becoming one with the Force after his death were planted a long, long time ago in A New Hope when Obi-Wan pulls a similar trick by disappearing after Darth Vader strikes him down, and at the beginning of The Last Jedi, when Kylo Ren says out loud to Rey that the effort of projecting across the Galaxy would be so great that it would kill her. It pays off when Luke projects to Crait to duel with Kylo, and the effort is so massive that, as Kylo said, it does indeed kill him.
It is tempting to play the shock twist game with almost any franchise; however, this specific way of tricking the audience has never been part of Star Wars toolbox.
Star Wars follows a very classic structure. In the prequel trilogy, the ending was foretold; the original trilogy followed a strict version of the Hero's Journey, and the sequel trilogy is also sticking, so far, to Propp's "Functions" of the fairytale. In this Galaxy far, far away, dead people are quite open about their state, even when those that died on the Dark Side of the Force would prefer to return to the realm of the living.
However, for those fans that want to see Luke as a ghost, not all is lost. There is a high probability that a spectral Luke will come back in The Rise of Skywalker, along with other friendly Jedi, to assist the heroes in their final showdown against (presumably) Palpatine -- or maybe even to celebrate with them at the end of the movie, as the dearly departed Jedi did in The Return of the Jedi when they crashed the Ewok banquet.