I find that a lot of players miss something crucial about the endings. My reasons are twofold:
ONE:
That very last part, where the Stargazer and their child are watching the stars, the Stargazer tells their child:
"Many of the details have been lost to time."
And the child asks:
"Can you tell me another story about the Shepard?" (emphasis added)
What this tells us is that the ENTIRE trilogy, all the way from opening scene of ME1 to end of ME3, has been a story told by the Stargazer to their child.
Let me repeat that, with emphasis:
THE ENTIRE TRILOGY WAS TOLD AS A BEDTIME STORY TO A CHILD.
Oral tradition, by it's nature, is prone to details being lost, especially after so much time. Much like the telephone game, you start with a sentence "the cake is a lie" and by the time it reaches the end of the line, you get "Kevin's gotta fly" or "I should go".
That's just with a dozen people, now think of how it has been EONS since Shepard and co. were around; it's not hard at all to see that no one really knows whether Shepard chose Paragon or Renegade, or any of the other choices you make along the way.
TWO:
The Reapers are defeated. Everything they represent is gone.
The death, destruction, the twisted logic of the "Catalyst" is no more.
Wasn't that the whole point of the trilogy, to stop the Reapers?
Whether it's direct (Destroy), subversive (Control), obsolescence (Synthesis), or postponed (Refuse), the Reapers are gone. THEY HAVE BEEN STOPPED. The galaxy is at peace, life has won.
TWO and a half:
It's YOUR Shepard, therefore you can insert your own headcanon and odds are it'll fit.
My Shepard is a full Paragon Vanguard/Sentinel hybrid (I'll explain in a note at the bottom, for those interested) who saved the Council, cured the Genophage, spared/saved the Rachni, Wrex and Eve lead the Krogan, Quarians and Geth made peace, saved everyone he could, kept his entire crew alive (as much as possible) and ultimately chose Synthesis.
My headcanon is that Shepard, having tapped into the power of the Citadel/Catalyst, was able to recreate his body (after all, it cures Joker's Vrolik Syndrome, why not a repeat of the Lazarus Project, aka coming back to life?).
Then he brings back the Virmire Survivor, Mordin, Thane, and all his other friends who died in the war.
With all the newfound knowledge held by the Reapers, he brings back the Protheans from their Collecter "shells" and brings back all those other races that were "Reaperfied".
Everyone remembers the mistakes of years past, what with the Asari holding back Prothean artifacts, the Salarians conducting secret experiments, the Krogan trying to fight everybody, and so on. No one wants a repeat of that, so an unprecedented level of cooperation begins to set in, and it endures. Racial boundaries dissolve, and while names are kept for the sake of simplicity, the galaxy is actually, finally, one.
It's a new golden age, and with Shepard and crew (all of them, from the whole trilogy, like during the Citadel DLC and the Party at the end) continuing to explore the galaxy, the adventure never really ends.
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To clarify, I'm not bashing anyone who hates the endings, I see their reasoning and it makes sense.
While the Indoctrination Theory would have been absolutely stupendous to have, it's ultimately not necessary, because I don't need to be spoon-fed a cinematic to have my happy ending. There is enough information given so as to form your own conclusions as to what "really" happened, and plenty of room for headcanon to fill in the rest.
I gather that a lot of hate for the endings comes from the fear of irrelevance, that your choices don't matter except for the one at the end where it's a four-way sadistic choice.
As my Shepard says: "I won't let fear compromise who I am."
So instead of being afraid that my choices mean nothing, I instead choose to see it as a means to finalize my happy ending, and all my choices during my journey determine just how happy it's going to be.
As you can see by my Shepard above, it's about as happy as you can get.
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NOTES: By Vanguard/Sentinel hybrid, I like to use Gibbed Save Editor to change my class, I use the headcanon that the Lazarus Project enables Shepard to effectively be any class he chooses, he just has to pick one at a time. So I go the medbay, save, change class, go back, pick a different bonus power, and keep playing. Whether I'm "officially" a Vanguard of Sentinel determines who is the Virmire Survivor (If Vanguard, it's Ashley, romanced. If Sentinel, it's Kaidan, Miranda is romanced)
That's just my way of playing it, since it is MY Shepard. And since it's my headcanon, I can finally be both and have both Kaidan and Ashley in my squad.