Note that none of the key philosophers around that time bothered with the "identity", it is a modern concept primarily driven by politics and exposure to outsid

Note that none of the key philosophers around that time bothered with the "identity", it is a modern concept primarily driven by politics and exposure to outside religions. So for none of them it was a fork. They all developed on the main branch, in the absence of centralized PR approvers everything gets merged. In India this identity matters even more as the Indian constitution offers different rights to you based on your identity and you get to benefit from "unequal laws" hence everyone deeply gets sentimental about it.