Of course Buffy's race was a defining characteristic. Just because she's not labelled "white" doesn't mean her whiteness doesn't define her. Her race is exnominated simply because she's of the racial majority. It's taken as the norm. Is she ever referred to as the white slayer (in the same way Kendra's referred to as the black slayer - genuine question)? In addition, any element of plot that foregrounds history/historiography (eg. Pangs) must tacitly acknowledge her race because PoC have a different relationship to history (and a different history) than white people. Look at Nikki in Tales of the Slayers who has a poster of Malcolm X on her wall. I do think the show made a bit of a hash of representing minorities but, as @forbuss says, it's self aware. Hence in S7, Buffy stereotypes Wood as "from the Hood" and we have Rona's comment "'Cause the black chick always gets it first?"I don't want Buffy's race to be a plot point or defining characteristic. It shouldn't matter what colour someone's skin is, unfortunately given the current climate, I doubt that Buffy's race won't be made into a storyline for an episode.
I take on board local demographics but (just been reading an article on flip zones) it appears suburbs in the US "have grown more racially diverse, more educated, more economically prosperous and more liberal". If that's the case, then the setting becomes the same but different. To be perfectly honest, I'd appreciate any reboot with a black Buffy that acknowledged racial difference. They can do a BtVS/Roots hybrid for all I care. I'd want to know what would happen if a black slayer had been called during slavery or the Jim Crow years. Race makes a difference. Look, for instance, at Walter Mosley's black private detective Easy Rawlins - he's written in the wise-cracking tradition of Marlowe and Archer but, because of his race, he has access to spaces they didn't (and is similarly barred from others). I'd hope for similar acknowledgement of race in a new BtVS. Lucifer manages it without being clunky (and the Lucifer writers acknowledge their debt to BtVS). Look at Hill Street Blues (10 years before BtVS and which, along with Mad Men, was nominated for more Emmys than any other TV series). It's not blind to race; in fact, from the pilot it makes race central to the narrative. In what way is that deficient or lesser TV (and yes - I'm aware of the different setting/genre so it's not a direct comparison)?
"Identity politics" existed before the term was invented!Identity politics needs to stay the hell away from any Buffy show. It's divisive and the moment a show starts going "woke" , the audience is going to start dropping like flies especially if they don't agree with the narrative and agenda being pushed.