Because I serve to live, I've been poking around a bit.
The arguments are:
1. Harris only recently decided she was Black (not true; she was president of the Black Law Student Association in law school, over 30 years ago).
2. That Harris only mentioned her blackness when it was politically convenient (which is a, well, weird thing to say, as if they expect Harris to say, "Hello, I'm an Irish*-Indian-Afro Caribbean female earthling" at every opportunity).
3. She's not really Black. (This involves listening to well, ackshully gossip that Harris' father was Irish and Indian, and not Black.)
* Harris' father claimed he was a descendent of slave owner Hamilton Brown (which an Irish genealogist confirmed). And Harris' father's maternal line also has Irish roots.