Concerning the third and last Roman-Jewish war, caused by the Bar-Kokhba Revolt (132-136 CE), repeatedly one can read: „The Christians sided with the Romans.“
That sentence makes hardly sense, because the Christians were an illicit religion in the Roman Empire at that time. So, such a gesture would have been as bizarre as a felon standing up and saying: „I’m siding with the state!“ Maybe one should grumpily add: Very big felons might meaningfully do so – but the Christian movement was still way to small to play any such role in early second century CE Rome.
„Siding with the Romans“ would not have been totally absurd for that era’s Christians, admittedly, because the mode of persecution of Christians applied by the Roman state was very peculiar at that time: As long as you didn’t cause any irritation, authorities were not interested – but if you were reported and then didn’t revoke, you were executed. We recognize this policy from a correspondence between Pliny the Younger and Emperor Trajan dating to about 110 CE. In that strange sort of situation, clearly some personal or group advantage could still have been won by collaboration with government.
There is no doubt, however, that the Christians could impossibly cooperate with Bar Kokhba, because he declared himself Messiah, whereas the Christians were defined by having their Messiah already.
It is important to understand that the situation during the first Roman-Jewish war, which commenced in 66 CE, was significantly different inasfar as the Christians were not yet an illicit religion at that time. After the catastrophe of 70 CE, the „Tannaīm“, those surviving Pharisees who became the founder Rabbis of Rabbinical Judaism, drove the Christians out of the synagogues because they were resolute to reinvent Judaism on a heavily disciplined basis. They clearly saw that the Christians would disturb that plan. As they perceived the situation to be a struggle for the bare survival of Judaism, the „Tannaīm“ were unwilling to make any compromises.
The prudent Jews had earned the gratitude of Caesar and Octavian during the Roman Civil War, and as these men happened to be the winners of this war (inasfar as a civil war can have winners at all), afterwards the gratitude turned into practical benevolence – hence the Jews’ status as „allowed religion“ in the Roman Empire.
Now this status was sort of a single ticket. Understandably the Romans didn’t regard schisms of religions which they once allowed as a phenomenon making the governance of their empire easier. Thus, they harshly confronted crisis-like diversifying 1st-century-CE Judaism with the demand to decide who was to get the ticket – you know what happens if you tear a ticket, it doesn’t make it two tickets.
Because in ancient Rome „unallowed religion“ wasn’t a nice status to be in, the fight for the ticket wasn’t amicable. The „Proto-Rabbis“ were the ones who won it. The trophy was the right to pay the new Roman „Fiscus Iudaicus“, which was invented after 70 CE. While Domitian, according to Suetonius, was still taking everything he could get from this tax, his successor Nerva during his short reign had hardly anything more important to do than to mint a coin saying „fisci iudaici calumnia sublata“. Although it sounds nice if you „end a calumny“, the true meaning was that from now on the emperor wanted to get a clearer picture as to who a Jew was and who not – in order to more precisely target with persecution those who were not.
In the inner-Jewish fight that arose after 70 CE, the „Proto-Rabbis“ spread the story that in the war the Christians had collaborated with the Romans. „Technically“ this would have been much more believable in the 60ies CE, when the Christians were still Jews legally speaking, compared to the 130ies CE; nevertheless, it stands out that the first Roman-Jewish war was followed by an internal Jewish propaganda battle far more intense than in the 130ies CE.
Consequently, the claim that „the Christians sided with the Romans“ is very doubtful as to the first Roman-Jewish war, and highly implausible as to the third and last one.