Actually problem I see coming from both sides is player hate, not character hate.
You created picture of each other as evil idiots that got to be shot, once you're able to get over it and get in characters head and not players head you'll be able to function normally.
I bet if you took any two factionalised people groups and put it instead OC and CR (to act as OC and CR) there would be no hate.
You have too many personal grudges to play nice or to act friendly, so you're swimming in your nice pool of hatred. The fact you can't make a huge 101st-CR skype group and discuss is there is fact by itself, public thread won't get you anywhere but to eventually flaming one another and pointing fingers.
Or your RP just became stale by non ending shooting each other in tau 23 situations, and if your RP is limited to only shoot each other then you do have a problem.
Now as I said my personal advice is make a skype group, with every member of said faction involved (not just high member ones) and talk, get to know each other.