More libraries are built. The government publishes the classics. Every library is provided with the classics.
Julian has a less fatalistic view about his own death. Julian does not die when at war with the Parthians.
The religious views of the emperor influence the views of citizens. The emperor which follows Julian is pagan.
None of the above conditions will turn back the clock. The influence of Judeo-Christianity cannot be completely erased. However, the world would be a drastically different place.
Perhaps the most important question is: how would the people of Judea be integrated into the Roman world? Tacitus viewed them as seditious. He said that they revolt as soon as they have the opportunity to do so.
Without Christianity, Judea is again at odds with Pagan Rome. The next question is: what are Judea's best options?
The Talmud was compiled in the 4th century A.D. There could be a timeline where the Talmud becomes more important than the bible. It could be seen as part of Judaism like otl or be perceived as a separate religion. Given the divisive nature of humans, with the absence of the bible, my guess is the Talmud would be perceived as heretical to the torah.
However, the conquest of Mesopotamia would be a variable that's particularly important. If Julian is successful against Parthia in Mesopotamia, there will be a dramatically different outcome than otl. Would the Talmud even exist today if Parthia had been pushed back?
Given the great divide between Judaism and Paganism, a collision course would have been set. Much like when Judea's temple was burnt down in 70 A.D. So how do the Jewish people fight for their survival? Their solution will not be force, rather persuasion. What sort of propaganda might result? There could be more messianic cults that develop. If so, then there would be a different version of Christianity that is persecuted in the 6th century and becomes popular in the 7th century.
Another option is that Jews would flee somewhere else. Not sure where. Would Iran be feasible? Otl, Julian handed over Armenia to the Parthians. Maybe the Jews would have fled there. Although, if Julian is more successful against the Parthians atl, then this is unlikely to happen.
Maybe Ethopia could become the new center of Judaism. Arabia might not be out of the question. I doubt the Jews could coexist with Scythia, but I could be wrong. Note, I use the term "Scythian" loosely, to mean northern mounted nomads. The term "Sarmatian" was a more contemporary term, but only denotes western Scythians.
Whether or not there's Messianic cult 2.0 emerges in Rome at a later date, or the Jews flee, would largely depend on the degree to which Julian is successful against the Parthians.
There can also be a remnant of Christianity which either independent from the Torah or Talmud or synergistically with one or both of these eastern writings forms a religion which is difficult to imagine today.
Further down the road, it's possible Jews make it to India. They may have done so otl. The word Baraita is a lot like Bharata and the word Bhraman could be derived from Abraham.
An earlier variable to consider is the question of Pharisees vs Sadducees. They have different beliefs. The Pharisees are more seditious than the Sadducees. The Sadducees do not believe in spirits and angels. The works of Josephus, who wrote about the Sadducees could become more important atl. Unlike otl, the Sadducees could produce produce works of their own. Considering their high social standing, they certainly had the means to do so. Note, Wikipedia does not make it clear at one point this group stopped being relevant.
Another group to consider are the Essenes. They blamed the fall of Israel on the impiety of the Sadducees. This group most closely resembles Christianity. One of the most remarkable things about them is that they chose not to own slaves.
The Essenes can be subdivided into two groups. 1. The 4th century Nazareans. They were vegetarian. 2. The Ossaeans came after them. Like the Nazareans, they forbade the book of Moses.
In conclusion, there are two main variables to consider: x. The degree to which Julian succeeds in Mesopotamia. y. Which Jewish sects dominate.
Someone with a greater Judeo-Christian theological understanding, in addition to more detailed knowledge of corresponding migration patterns, might be able to better determine what sort of propaganda would result from changing the variables mentioned above.
Note, variable y is dependent upon variable x. Whereas, religion/propaganda is a third variable, dependent on the other two. Alternatively, flight is chosen over intellectual fight.
Ultimately, pagans are likely to get outfoxed. Julian will not be able to change this. Nevertheless, there could be more great classical works written before the fall of Rome.
One less work that would be written is Boethius. Although, there could be a similar writing depending on the nature of a delayed collapse.