Rejecting caste while still calling oneself Hindu is incoherent

Evidence

But it is pertinent to ask what the Mandal believes in, if it rejects the shastras. How can a Muslim remain one if he rejects the Quran, or a Christian remain Christian if he rejects the Bible? If caste and varna are convertible terms, and if varna is an integral part of the shastras which define Hinduism, I do not know how a person who rejects caste, i.e., varna, can call himself a Hindu. — Ambedkar, B R, Annihilation of Caste_ The Annotated…, 1212

Categorization

• XREF: This is Ambedkar’s core argument that what defines a Hindu is varna/shastras, hence ‘I had the misfortune of being born a Hindu’; his leaving is not rejection but consistency.
• QUESTION: Under this logic, what could any reformer who rejects shastras legitimately call themselves — and does this make conversion or a new religion the only coherent anti-caste stance?