At this point I think you’re just defining schism differently than I am.
To me, Conservative Judaism is a schism because their innovations ARE purely about breaking halacha. Chassidim vs. Litvishers are just two brands of Orthodoxy/Torah-Judaism. That would by like saying Ashkenaz/Sphard is a schism.
“there is no system for it.”
Sure there is, elu v’alu divrei Torah. If someone does something different because their part of another “group” (eg. they daven a different nusach) that doesn’t mean you hold that they’re wrong. By the way, I should probably point out at this point that I’m not agreeing to you lumping female rabbis in with completely uncontroversial philosophies as if it fits with them and is of equally little consequence. That issue actually does have halachic ramifications.