I love this topic.
I actually think Christianity was larger than 10 percent by 300AD
if we are to believe that at the time of Christ 10 percent (!) of the Roman Empire was Jewish. TO have such a high number, many of these Jews were not Hebrews but rather Gentile converts. And, if we read Acts of the Apostles, it is obvious that Paul found Jews "in every city" and his success was in converting the Gentile Jews over to Christianity. THere was a big reason for this, as it was a Jewish religion that did not require circumcision. The circumcision controversy in the early Church was not small and all but two of Paul's epistles mention arguments with Jewish Christians who insisted on circumcision. So, in short Jews (even the Christian ones) really did not Gentiles to be full members of their communion without circumcision--Paul, like a reformer, said hogwash to this and this led to mass Gentile conversion. Hence, shortly after the time of he diaspora, it is my belief that most of the gentile Jews converted to Christianity, especially as the whole focal point of the Jewish religion (Jerusalem) disappeared.
This means Christianity was upwards of 10 percent of Rome by the mid second century. Even if this is too rosy a view, we have certainly exceeded this number by the third century. If Dionysus of Alexandria and Eusebius is to be believed,
at least two Roman Emperors during the third century appeared to be cradle Christians, though they appeared to have apostatized as adults. Cyprian in the mid third century writes of financial corruption. Also, during the mid third century, Paul of Samosata at patronage from Zenobia (leader of a large rebellion against Rome). THe next Bishop of ANtioch had imperial sanction. All of these things are consistent with the idea that Christianity was a rather larger religion, especially in the cities.
I have heard the numbers that Christianity was 10 percent of the West and 50 percent of the East by the time of Constantine. I would venture to guess that it was considerably higher in the West (high teens) and lower in the East (high 30s). But, being that Helen (Constantine's mother) was a Christian and likely brought up Constantine in a matter akin to Monica bringing up Augustine (Chritianized, but not religiously so in order that he can be trained for his career) this speaks to Christianity pretty much being everywhere, from the oppressed North African peasant to the wielders of power in Rome.
In my opinion, Constantine only began officially tolerating a religion that was so big, that to not do so seriously compromised the size of Roman armies and their tax base. Christianity was probably 30 percent of the entire empire at this point and they took their religion more seriously than the pagans, who themselves were split between Gnostic sects, eastern mystery religions, and local folk religions. Propping up the imperial Roman religion was becoming untenable. There's a reason why Romanized lands, like Armenia and Georgia, later Ethiopia, were going Christian with the hammer of the Roman state. This is also why the Parthians had to so strongly resist its growth. Christianity was already making big waves with or without state influence.
Constantine co-opted Christianity and later the Edict of Thessalonica essentially made it a sacralist institution (i.e. new state religion/imperial cult.)
So, what happens to Christianity without Constantine. Obviously, some later Roman Emperor will go Christian. And consistent with every other people that has gone Christian, they will make it the state religion and what we have today is pretty much the same as what we had in the past.
However, is there a way to maybe, just maybe, delay imperial sanction in favor of Christianity in order to make it anti-sacralist and change the face of Christianity? Maybe.
Here's my POD. Helen gets murdered and Constantine does become Roman Emperor, but not Christian. He does move the capital to Byzantium. His sons likewise see to the east-west split of the empire. Here's what I think happens.
-Donatist schism occurs, a Council in Rome excommunicates them but without imperial sanction of the excommunication, Donatists remain in communion with some churches. The schism blows over after a few centuries until only a few hold outs, like the Novationists, are still around. This occurs with a Punic, as opposed to a Latinized, Bishop of Carthage eventually getting the See.
-Arianism still gets anathematized, but local councils and letters exchanged between the metropolita. No Nicene Creed is made. However, the Apostles Creed (which the Nicene Creed is based upon) may be cited as evidence of the orthodox view and this leads to increasing standardization.
-Germans are evangelized as orthodox simply because Arianism is not anti-nicene and there is no political reason to go anti-nicene.
-Great theologians like Hilary of Poitiers, Athanasius, and Ambrose start concocting systematic theologies, as do the Cappadocean fathers, and Augustine after them.
-Sometime during this point, we need some great saint to be martyred in another persecution. In this saint's writings, he must reject imperial power explicitly. In OTL, we seen Cyril of Alexandria's theology in five years after his death become endorsed by the whole Christian world. So, I think this is something cultural that can happen.
-An ATL Emperor goes Christian and ends persecution. To make this timeline work, he has some sort of religious experience that he believes he is patronized by the anti-imperial saint and simply allows for the toleration of the Christian religion. At this point, ATL Council of Serdicia and the precedent of Egyptian Bishops appealing to Rome makes the Roman See the final court of appeals. Constantinople, not the seat of any official Patriarch, cannot lay claim of this especially without state support.
-A Papalist system arises where the Pope is the final court of theological appeals, but his decision must be ratified by councils and a consensus must be forged.
-THis system must become strong enough and entrenched enough that by the time Christianity gets imperial sanction, the Pope's and the Council's power are so independent, that the Emperor at best ratifies their decision into imperial law and jockeys to pay off the Bishops.
Now, my stream of consciousness reveals that we eventually revert back to sacralism, even with everything going against it as I am trying to do above. Perhaps, if we can make it agreed doctrinally during the 4th century that political authorities cannot appoint bishops (simony already existed), that we can get rid of half of the corruption but not all of it. However, if states cannot appoint bishops because the Church universally rejects this as heresy, we can avoid overt state control, even as the religion gains precedence in the whole western world.