I apologize for coming across disrespectful before, I was tired when I wrote that first post but this theory does have a lot of stereotype to it in the Roman Religions.
My point is that not being in the Cult of the Emperor did not present a threat to the ideology of the Principate, the emperor was not a "God Emperor" if he was alive, and finally whatever ideological reason to persecute Christians existed for Diocletian also existed under the tolerant Emperor Aurelian, and certainly existed in the first years of his reign. The only possible examples of Principate God Emperors available are Bad Emperors. The Romans didn't revere living emperors, a Caligula, Domitian or a Nero could try to become revered but trying to be revered while alive had a literal 100% chance of death during the Principate. The relevance is this shows that Pagans did not revere living people in any religious sense of the word, they found self declared godhood offensive.
Now on refusal to participate in the cult that threatened nothing. Decius' edict was for everyone to present one sacrifice to "their chosen gods" it didn't have to be the Cult of the Emperor, and Diocletian ordered sacrifices to the Olympian Gods (Source Goldsworthy, How Rome Fell). Note that even if the Christians obeyed Decius' edict they would not have helped the unity of the Empire. There is even evidence that Decius' edict wasn't aimed at Christians and Decius did move to try and alleviate the pain he was causing them before he died. Note that had Christianity involved animal sacrifice to God the Christians could have complied with the edict.
The idea of Christianity undermining religious unity is intriguing, but the evidence is sadly lacking. The Pagans themselves did not revere living emperors, and on dead Emperors there was never any attempt to force Christians to present sacrifices to them specifically.
Religiously speaking the Pagans were as disuinited when Constantine came to power as they were before the Empire began. It is true that the Cult of the Emperor had more to do with politics and loyalty to Rome than any sense of religion, but there were other ways to show loyalty than a sacrifice. Note the level of tolerance before Diocletians edict, the martyrdom stories range from peasant women to senior centurions to senators, there were great churches Diocletian demolished and the best of all is the fact that the Pagans knew exactly where the Christians were and when to find them, and many of the martyrs had enjoyed imperial favor under earlier emperos, one elderly Christian Patriarch had actually pleaded for an earlier emperor to evict a deacon who had offended his congregation.
I'm sorry but my points are
1. Not enough Romans took deification seriously and the living couldn't be deified, so when sacrifices were called they were usually towards any Gods even if the state would prefer a show of loyalty to piety
2. There was too much tolerance, out of the few examples of intolerant persecuting emperors one (Decius) wasn't purposely targeting Christians, and the Romans seem to have found the Christians way too easily in Diocletian's reign. Saint George is probably the best known openly Christian martyr who took only moments to find because everyone knew he was a Christian and where to look. Perhaps Diocletian suspected Christian loyalty, but if he did why did he wait for later in his reign to persecute the Church? Wouldn't it have been responsible to start from day one?