The Palmyrene empire would likely be the first to adopt Christianity as state religion don't you think? And if it is in prolonged hostilities with the other empires, the spread of Christianity in them may slow.
I don't know how this might affect the later potential conversion of the Goths and Germans. I would figure there would need to be a "beach-head" for Christianity in Europe, like Thrace or Crimea, for missions to Goths and Germans to even be a thing.
What if we went to the other extreme and had the crisis of the 3rd century not just split but also collapse the western Roman empire. Who would shape the post-imperial destinies of Pannonia, Illyria, Gaul, Hispania and Africa. In what ways would it mirror or differ from the politics of OTL's 476 AD onward?
Well that's even assuming that Palmyra even adopts Christianity, and Christians have been going on throughout the Empire for quite some time anyway, so there is no guarantee that Gallia or Roma, assuming the former is still around, wouldn't adopt Christianity first.
As for, assuming the rest of the Empires break up further (say into Illyria, Gaul, Africa, maybe even Macedonia & Pontus), that I cannot say. I just say, good luck to the poor schmuck who's got to put it all back together again, assuming the Germans don't get to them first..