When the head of the military and the head of the religion are the same person, who was appointed, not elected, theocratic dictatorship sounds just fine. Source? Again? Or are you just brushing over that, too?
Tyrande, now high priestess of Elune and Malfurion's mate, implemented sweeping changes throughout night elf society. She organized a new all-female army, the Sentinels, and decreed that it would be directed by the Sisterhood of Elune. Nobility and sorcery were now considered the relics of a decadent and shameful past.
From the Warcraft Encyclopedia
As Tyrande is the leader of the Sisterhood of Elune (and the Church of Elune), she is leader of both, and technically would be considered a dictator (Though the historical dictionary definition for her is that of a Tyrant. She did basically Usurp the throne from Azshara and all)
However, this history does gloss over a few facts that are rather important. First off, Tyrande became leader of the Night Elves because everyone else bailed on her.
It was originally a joint held position by Malfurion, Sunstrider, Shadowsong, and Tyrande. Malfurion and the druids all but abandoned the Night Elves, and the Priesthood refused to reign them in, which led Jarod to become disenfranchised with the Kaldorei government, and he left. We should all be familiar with Sunstriders tale.
Tyrande rules the Night Elves because she was the only one with a strong enough sense of responsibility and strength of vision to do so. Sunstrider, were he still alive would fit into this boat as well, but they kinda had different ideals.
Malfurion and Jarod, as great as they may seem, kinda just ran away.
Not when they will know directly that they were trolls and only separated because of arcane usage. (Zandalari banned it or something)
It's a moot point right now though because any of this can change.
As mel said, nothing changes. Arcane kicked off the mutation, Elune shaped them. This is pretty much what the Night Elves always believed (just at one point attributing the powers of the Well to Elune).
Is their faith going to color certain aspects? Yeah. I mean, they thought Cenarius was the son of the Moon and the Sun (War of the Ancients, book 1). Facts are going to be mixed in with myth.
As is, it's highly likely that many Night Elves knew they evolved from Night Elves, and it's almost guaranteed that Tyrande did, considering she led the Sentinels policing Ashenvale forest and Hyjal for 10,000 years and Dark Trolls lived in both Ashenvale and Hyjal.
I think it highly likely that the Dark Trolls had their own pantheon of Loa, of which Elune was one of them (and I use Loa as a title, not a power level.). We already know they have multiple gods.