This could be a totally false premise.
In all my time reading history I have never read of such doctrinal conflicts occurring in societies that were polytheistic.
I think your premise is false:
According to the German Wikipedia there was a crime named "asebeia" in ancient Greece. People saying some religious convictions that were not compatible with the official religion were punished. Wikipedia lists six famous people that have been accused. Two of them - one of them was Socrates - were executed. We don't know how many non-famous people were accused.
In ancient Rome you could get the death penalty when you refused to take part in the imperial cult. The persecution of Christians was sometimes justified with this. The imperial cult however is a religious matter.
According to a TV report about India a few years ago there are Hindu groups which attack other people if that people do not live (for example: dress) the way these groups think that the Hindu religion requires it.
In all three cases we talk about religiously motivated violence by polytheistic religions.
So my question is what made monotheism so prone to intra-religion conflict as opposed to polytheism?
It is hard to say if this premise is true:
Every religion has something like "dogmas": If you don't believe in them you are not believing in that religion. This is of course also true for polytheistic religions.
The crime named "asebeia" in ancient Greece is the best example that believing that some of these "dogmas" is not true is also not accepted by polytheistic religions.
You mentioned Arianism in your question. Both Christianity and Hinduism believe that (a) god became a human and lived as human on earth. Arianism is a flow of Christianity that denies exactly that.
Not knowing Hinduism from the inside it is very hard to say if a Hindu claiming that Chrishna was a regular human would lead to stronger or weaker conflicts in Hinduism than Arianism did in Christianity.
... the doctrinal violence of byzantine christianity
Let's compare the "violence level" of the Christianity before becoming the state religion of Rome to the "violence level" after this time:
Before this time there are nearly no reports about religiously motivated violence by Christians; after that Christianity became very violent.
Today you can see that in many countries where the governments (mis-)use religion to legitimate their reign.
Once again we would have to compare to a polytheistic religion being (mis-)used by a government to legitimate their reign. Otherwise we have no real comparison between polytheistic and monotheistic religions.
Again this is about christians fighting christians not about pagans fighting christians.
When governments legitimate their reign using religion it's typically not a question of "intra-religion" or "inter-religion". Anyone who doubts the government's understanding of the religion lives dangerously.
Edit
I'd like to address the second comment of ed.hank because I think that my answer was a bit misunderstood:
but it still disagree that the asebeia in ancient greece rose to the level of a violent schism
As far as I understood the question correctly, it is not about the extend of violence but about the roots and the reasons for it.
And if I understood correctly, the premise of the question was that conflicts arise from inside monotheistic religions; the premise was not that such conflicts come from outside.
As I already wrote, my knowledge (which may be wrong) is that Christian religion was not violent until it became the state religion of Rome. After that point in time doctrinal conflicts leading to violence became quite common in Christianity nearly immediately.
For me this is an indication that the phenomenon of serious doctrinal conflicts did not arise inside the Christian religion itself, but that it was brought into the Christian religion from the (polytheistic) Roman culture.
... which would be exactly the opposite of the premise.