I'm not saying they're not different. I'm talking about the fact that they are ultimately labelled as "half-human, half-youkai" in IN's ending because they don't know what else to call them, and CiLR says they're originally from Earth.
Well, if they are 'half human, half youkai'
like Youmu shouldn't they be able to use the swords? Phantoms/ghosts are also considered a type of youkai. If a 'half human/half youkai' like Youmu can wield the swords, then 'half human/half youkai' like the Lunarians and Immortals should be able to use it too.
Not to mention that Mokou. Kaguya and (possibly) Eirin became immortal after drinking the Hourai Elixir.
I see becoming Immortal (even through Hourai Elixir) is like a next step in evolution. Same goes for Lunarians. They are more evolved than humans. You know that animals can eventually be unable to mate with each other once they start to grow too different from each other. Once that happens they aren't the same species anymore. A mouse species that consist of one colony can be split in two by a river that suddenly forms in between the colony. Each side keeps living on, doing their thing in slightly different environments. After 50 years or so the river will have dried up and the two mouse colonies can get together again. However, both mouse colonies, due to different environments, have grown to be greatly different from each other (like one side has obtained long snouts while the other side have way bigger bodies). They have grown so vastly different that they cannot mate anymore, turning them into two separate species of mouse. Humans and Lunarians can be compared to this.
The Lunarians have become so different from humans that you cannot possibly classify them as humans anymore. They are more youkai than anything. Thus, they could use weaponry that cannot be wielded by humans, since they aren't the same species anymore anyway. Hourai Elixir can be described as a quick short cut to semi-Godhood. They are more youkai/god than human. In fact, Mokou attained many youkai qualities when she consumed the elixir: her phoenix traits. The Hourai Elixir turned her part phoenix youkai, giving her the power over blazing fires. She is also FAR more physically powerful than normal humans. That sounds like 'youkai' to me in my book. Mokou is different enough to be able to use the swords.
Mokou is actually more youkai than Youmu! Youmu relies on her phantom half and swords: she doesn't have any innate powers like Mokou! Youmu's ability: swordsmanship and concentration. ANY human can learn that with enough discipline, even outsiders. Mokou's ability:
CONTROL THE FREAKING PYRES OF HELL! No normal human can ever hope to learn that without the help of magic, and even then they may never be able to use it as efficiently as Mokou! So, who is more youkai? Youmu or Mokou? I think the answer is obvious.