Playing a pure Dogmatic run and you'd kill/imprison half of the companions and a significant amount of quests. The game seemingly corrals you into Iconoclast.
Just because you can, does not mean you should.
I have 2 parralle runs one is pure Domatic the other is pure Iconoclast.
I have not handed Idira over to the inquisition. Yet.
Jae is in my Dogmatic's retune to atone for her sins by serving Empire.
Who else would you like to spare - the perverted space elf? Or another perverted space elf?
And Iconclast acts extremely retarded at times.
For example, you see a band of mutants with tongues covered with underdeveloped teeth kill your crew member for his boots.
Iconclast option: "Poor souls, you've never seen kindness in your life, here's a coin for you".
Dogmatic has only the Emperor's mercy to give and gets more positive effects.
My Dogmatic Commisar can pray at the ship shrine to get a buff, my Iconoclast Noble has no such option.
Iconoclast got a permanents debuff after saving people off Rykad, the Dogmatic got a good night's sleep after Exterminatus.
So far (Act 2) the largest difference I've seen is the pirate's inheritance quest.
But it's mostly tied to the way you arrive to Footfall, not your alignment.
All in all Dogmatic feels as "canon" and more fun way to play.