Yeah normally how my characters get along with companions is defined by the core beliefs I end up giving them, and each game my characters are fairly different I think. My Warden was ruthless and pragmatic who based every decision around what would be best for defeating the darkspawn. Didn't really get along with Wynne, Alistair or Leliana since they were too idealistic and they got mad at the decisions he made like preserving the anvil, encouraging Avernus to go full throttle with the research, wiping out the Dalish for Werewolf allies and stuff like that, (Heck my Warden ended up allowing Alistair to be executed since he attempted desertion when i spared Loghain to make him a Warden)
My Hawke despite not being a mage was pretty much all for mage rebellion, didn't like the Chantry or Templars all that much at all, and come to think of it was pretty fine with deals with demons and blood magic, so got along with Anders and Merrill but not Sebastian or Fenris though he ended up executing Anders at the end since despite having no love for the chantry or the templars, thought what Anders did was idiotic since it would have severely harmed the rebellions image and prevented them from acquiring any allies.
My Inquisitor on the other hand is actually quite conservative, sees the value in the Chantry, tries to be as diplomatic as possible and not change the status quo too radically, which I suppose is ironic seeing as he is a Dalish Mage. Got along well with Vivienne and Cassandra, not so much with Solas.
Each of them touch upon my own beliefs, but then go a bit further. If I were playing my characters based on my own opinions I would be diplomatic and cautiously against radical change like my Inquisitor, but still see the need for reform and sympathetic to the mage rebellion, as well as seeing blood magic and demonic deals as nothing but tools so long as done cautiously & properly like my Hawke, and ruthless + pragmatic like my Warden so long as it doesn't cost me too much diplomatically Unlike my Inquisitor I would probably get along well with Solas but not Vivienne, unlike my Hawke I would not get along with Merrill or Anders, Wynne i'd probably be somewhat neutral since she sure is preachy, and would get along with Alistair and Leliana