Let's just say that Kaguya's curious enough to touch a hypothetical interdimensional anomaly in the Hakurei Barrier. And Mokou... well she just won't let Kaguya go anywhere without her like when Kaguya returned to the moon some thousand and few hundred years ago.

And as for the UMMA... Yep I could see how people would rebel against it when it would willingly interfere in the affairs of two civilizations.

Planet A representative:
"Our planet is freezing up, we asked nicely for them to share some living space, they declined. In order to save ourselves we have declared war"
Planet B representative:
"And we will defend our lands from your invasion, we are honorbound to do so"
UMMA:
"No fighting in the house... that's final"

Sort of a comical way that's portrayed.