I've seen some interesting posts regarding why Luke dies in Star Wars Episode VIII The Last Jedi, and also how Force Projection works and the similarities between Force Ghosts and Force Projection. I was left very unsatisfied by Luke's death because the reason for it isn't apparent. It's possible the strain of Force Projection is what killed him, but that reasoning doesn't sit well with me. Maybe Force Projection is an ability gained by a Jedi Master after or during the transition to Force Ghost. I prefer this idea, since it would mean Luke would have had to have had one foot on either side of Life and Death to pull it off, and certainly we know of no one who's returned to Life after gaining the abilities of a Force Ghost.
Something to note is that the first time Kylo and Rey do their force communication thing, Kylo at first thinks Rey is using Force Projection but then he realizes she isn't when he says to himself “You're not doing this, the effort would kill you”
So to some extent early on in the movie they set up that Force Projection over long distances could be fatal.
That's not the first time we see this kind of death. The first time was Ben Kenobi during his fight against Vader (Star Wars IV: A New Hope), and Yoda after the Jedi training of Luke (Star Wars V: Empire Strikes Back). Both of these deaths seem to be on purpose or like an accomplishment(Ben's death to let Luke handle the suite and give him motivation? And Yoda's death because he finished training Luke)
We can see other kinds of death that are more "traditional" (without the disappearing effect) in the different Star Wars movies (for example: Qui-Gon Jinn) but they don't seem as peaceful as the others I quoted.
So, I think the death of Luke was not due to the projection but because of his accomplishment in helping the Rebellion for the last time, like a redemption for his disappearence during the past 10 years (not sure of the time).
Yes, it contributed, but it may be philosophically debatable what the IMPACT of "choosing" to die a particular way means for a Jedi...
"I don’t want to get too explicit, because I like people being able to have their own interpretations. But I think definitely the act of what he does at the end literally just takes everything out of him. That’s a huge thing. Also... he’s having his final act be something of myth-making in a way."
Of course, we said "final scene" and not "death scene" because there's always the possibility that Luke could return as a Force ghost in Episode IX, which J.J. Abrams and Chris Terrio are now writing, with Abrams to direct. Johnson agreed that the son of Skywalker could indeed make an encore, saying Luke's ending in The Last Jedi "seems like it just gives you a whole other realm to get into if [Abrams and Terrio] chose to in the next film." http://www.syfy.com/syfywire/rian-johnson-what-really-happened-to-luke-last-jedi
Rian Johnson has said that Luke astral projecting did contribute in exhausting Luke, but clearly, given what we have seen before with older Jedi Masters (Obi-Wan, Yoda), Luke also "chose" to become one with the Force, given the way his body disappeared/dematerialized.
When other Jedi characters either do not choose to and/or are unprepared to die (Qui-Gon Jinn), their body is left behind and it may be harder for either their Force Ghost to come back and/or for other Jedi to communicate with them in the netherworld, as it appears to rely on several factors such as training and/or metaphysical geology in some cases.
"It is I, Qui-Gon Jinn." "That cannot be. Dead, you are." "No. I am part of the Living Force, Yoda." ―Jinn communes to Yoda during the Clone Wars
Revenge of the Sith - Transcript
YODA: Master Kenobi, wait a moment. In your solitude on Tatooine, training I have for you.
YODA: An old friend has learned the path to immortality. One who has returned from the netherworld of the Force. Your old master.
YODA: How to commune with him, I will teach you.
Over the past few years, Star Wars "force ghost" mythology has expanded from the Prequels to Star Wars Rebels, to the new trilogy and so on.
One of the really cool advances and unique juxtapositions The Last Jedi added was show viewers an astral projecting Luke, who choses to die at the same time as NEARLY MATERIALIZED Force Ghost Yoda, along with the sudden departure of Snoke.
With Yoda's advancement, it becomes clear that Force Ghosts may be able to play much bigger roles than one may have previously thought; -now being able to more heavily interact in some [metaphysical] spaces!
But to further conclude, this advancement may mean it is not The Last Time one may see either Luke or Snoke (remember Snoke is NOT a Sith and it's unclear what his beliefs with the Force are or originate), let alone they may be able to more aptly pyschically interact with the other characters. Rey and Kylo Ren seem to be a part of some yet to be disclosed force mythology where each has some "raw" power that goes beyond traditional force sensitive beings, thus the stage is "ripe" for these particular dynamics to occur.