Actually thinking about it, Sariel existing at least implies that Judeo-Christian angels exist in the Touhou universe. If you really wanted to make Christianity work in that context, you could say these angels are akin to the Shinto gods we see in Touhou, and then just keep it ambiguous as to if they actually follow some all powerful true God or if it's just a sham they perpetuate to consolidate spiritual power.
That's the only way I could see Christianity working in Touhou without just entirely misrepresenting Christianity like TLC did.