In reality, at the time, it was the Eastern Christian church that was more liberal than Rome. Rome insisted every local church make services in Latin, and didn't translate it in the local language.
The Eastern church instead, had the bible in Greek, but allowed to translate it in local languages and make services in them. Initially, those translations were made with Greek letters, which weren't fully reflecting the phonology of Slavic and other languages, so they were extended, which produced Cyrillic.
As I understand, the same way Coptic script in Egypt, and Ge'ez in Ethiopia were made, thanks to Eastern Christian church allowing this.
p.s. Saint Cyril, in fact, invented the Glagolitic script. Cyrillic was named after him, and initially "Cyrillic" alphabet was mostly Greek, plus some characters from Glagolitic, like Ⱎ, ⱍ and ⱑ.