I see many people responding with an an argument "they are only projections of already dead people, so shutting them off is not morally evil".

I agree to that and don't argue. As I wrote, most likely Endless are just glorified chatbots, so shutting them off is objectively not more evil than deleting a game from your PC. Most likely, as we cannot be 100% about their nature, since many things about aether and souls are vague in ff14.

However that misses the main point of my argument: evil or not, we simply don't have neither authority nor legitimacy nor right to do as we please in Sphene's kingdom. Even if existence of Endless is in the end harmful, as long as Sphene doesn't use outside souls for her system, we have no right to intervene. What we have is the right to stop her from threatening souls outside, by force if needed. Erasing Endless within their bubble, however, is an internal affair, a decision that must be done by local legitimate authority, not by us, a hostile outside force.
And if we say that we allowed ourselves do to as we please in Sphene's realm because of situation in extremis, that makes us somewhat of a war criminals, since we were targeting civilians which has no direct effect on stopping Sphene here and now.