Julian II (the Apostate) and his policies

[TITVS SABATINVS AQVILIVS]

I'll avoid to enter the religious aspects of Christianism because it cannot be discussed in RAT, so I'll limit myself within the political aspects of the discussion. If you like to go to "religious" we can do it by PMs.

Additionally Christianity had a strong organisation,

True.

brilliant intellectual support

Not true.
Nor in absolute, because where an intellectual support exists is practically copied from classical and "pagan" sources, nor if compared to the whole corpus of the "pagan" one, greatly superior.

and an aggressive behavior towards other believes.

Yes, that's absolutely true.

It had a fast growing base of devotees even before Constantines helping hands.

That's oversized by the christian authors.

After Nicaea the furious fights within Christendom ebbt a little bit, making the mainstream stronger than before. So my believe is that in the middle of the 4th c. AD Christianity was already too strong to be subdued.

That's not true, Christians were so few yet, compared to the "Pagans" especially in the countryside of the Empire, in 399, in the Codex Theodosianus, was said to destroy the remaining pagan temples in the countryside, and Honorius in 408 said the same. They felt the need of destroying pagan temples by law in 408 yet! And we know that "Paganism" was diffused enough to worry the Christians till a lot of years after. Julian, when Emperor, went with the bishop Pegasius to the Herôon of Hector, to the Athena Ilia, and finally to the Achilleion, found them still perfectly maintained. Pagans were a lot yet, just they were less fanatic and violent than the Christians, so less visible. A man like Iulianus, an Emperor with a faithful army (let's not forget it), could easily be their new leader and give with very good chances strenght to their resistance. Exactly like Costantinus give strenght to the Christians. So, Christianity was not already too strong, it was just already screaming a lot.

Beneath religion the classical political ethos had nearly ceased at that time. It would have been a very difficult task to revive it in the structures of the Dominate. The future belongs to the absolute state in the form of the Christian Byzantine Empire and the near-feudal structures, where no longer the private interests seek completion in the state but the "state" becomes a private affair.

Iulianus' project was about an absolute but liberal and just State, so perfect for the times as well.

So there was no real mental base for the fight against Christianity. With military suppression alone a struggle for the minds and souls of the people was not to win.

Exactly, Iulianus' project was not based on military suppression.
In my opinion the truth is that if Iulianus was not hit at the back (and not by a persian), and seen his incredible skills, practical and spiritual, he would have had good chances to make a conservative revolution up to invert the christian trend/fashion.

Vale,