Except the cult's goal isn't coexistence, they want the invaders to rule humanity
correct, but it's his
personal idea of coexistence- as in he earnestly believes it's the best thing for the world instead of rangers wiping out invaders and continuing their masquerade.
Of course, his idea is obviously villainous, but considering there is clear corruption in the rangers - especially yellow and red, he does have a point.
they want the invaders to rule humanity, which both Sakurama and Hisui are against.
incorrect , Sakurama is ok with that, he specifically told D he's ok with mankind being conquered if pointless war ends:
https://mangadex.org/chapter/996561b1-9be4-4f71-8376-ea53a087be3d/13
It's dumb for the cult leader to expect them to switch sides just because he told them the rangers are losing out there.
as I've mentioned, he's not specifically telling them to fight for IRA, but probably just feeling 'generous' because he has extra mass-produced stuff, and XX vouched for Sakurama.
As for Hisui , she is just too strong-willed and heroic for his persuasion, his persuasion
could have worked on some weaker-willed rangers like what happened to Wakaba (who joined magatia)