AHC: Persia adopts Christianity but Rome doesn't

I have a question ? If roman empire doesn't take christianism, that means that when it falls no papacy and no christian kingdoms ? So eventually, how would affect Islamic conquests, admitting that RE fall and the arabs crush the as OTL, won't that make it easy for them to conquer their way around Europe.
If Rome doesn't adopt Christianity, butterflies would probably make it so Islam doesn't exist.
 
I think, that if Persia adopts christianity, it would lead to a conflict between the zoroastrian clergy and the Shah, and thus would result in a risk of civil war much earlier than before.
 
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