Muffin:
If people start thinking that fanon takes precedence over canon, when someone says "Eirin is Sakuya from the future, who left the SDM after Reimu slew Remilia", none would be able to say otherwise, even if canonically Reimu didn't kill Remilia.
Donut:
perhaps Eirin is human, it all depends if she was always living in the moon, or she moved to the moon (much before Kaguya had to be exiled to Earth), it's a possibility; Kaguya, however, has a greater possibility of having been born in the Moon, though
Black-Cat:
Nue said she was imprisoned until after Subterranean Animism; unless you consider the possibility of Yuka being imprisoned right after PoFV D: