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Terfs by definition exclude women and are therefore not feminist. Hate groups often try to legitimise themselves by adopting more reasonable names even when it goes directly against their views, eg “All lives matter” formed specifically to counter the claim that black lives matter.
Yes, because the person you replied to is either wrong or lying (some terfs claim terf is a slur). Terfs do self-identify as terfs. A recent prominent example would be Sall Grover, “During this incident, Grover self-identified as a trans-exclusionary radical feminist”.