There's a few things you're forgetting/ignoring...
1.) The nature of life in the universe.
For something in the world of Final Fantasy XIV to be alive, it has to have three things; a body, a mind, and a soul. This isn't an opinion; it's a scientific fact. This is why ashkin (undead) aren't alive; zombies and skeletons have bodies but no souls, while ghosts are souls with no bodies. Since Endless lack true bodies and souls, Endless are not alive. Hell, we're told as much. By the Endless.
2.) Emet Selch was a racist.
While you are right, that Emet Selch thought we really weren't alive, it was because he thought we were inferior. His whole talk about how we're "insects" mirrored similar views that people have used to justify genocide in real life. Since even if our souls were less dense than his, we still had souls. We were still alive based on all definitions of life, in universe.
3.) The Endless are essentially ghosts with questionable sentience, let alone sapience.
As mentioned above, with ashkin, the Endless are ONLY memory. No body, non soul. Basically, digital ghosts. When you shut down the terminals, you're flat out told that some will remain behind if they have "unfinished business". And while some of those that remain do seem to realize other people have disappeared, they seem unaware that the world around them has changed to a shade of grey.
4.) Our actions are defined, in game, as a tragedy, but really the ONLY choice.
We're not doing what we're doing out of malice. We're doing what we're doing because it's the only thing we can do, in order to shave our world and other worlds, because the Endless are unsustainable. If we didn't do something, everyone in the Source would die, as a sacrifice to keep around the memory of the dead. And eventually, it would spread into other sources... And eventually, in time, still fail, since their isn't enough energy in the universe to keep the machine running indefinitely. So in time, a countless number of lives will be lost and everything still ends the same.
4.) Emet Selch was a racist.
While you are right, that Emet Selch thought we really weren't alive, it was because he thought we were inferior. His whole talk about how we're "insects" mirrored similar views that people have used to justify genocide in real life. Since even if our souls were less dense than his, we still had souls. We were still alive based on all definitions of life, in universe.