Regarding race, Constance's best friend is black, and she married Constance's brother. However, I imagine she is from a rich family in order to have been in the same circles as Constance.
IIRC, Constance also fell victim to a cult, moved to Nigeria and fell in love with one of the cult leaders. I think she has a preference for black men.
Her family probably objected to MG's criminal background, age gap, probable drug use, lack of means, and the speed the relationship progressed at rather than the race.
I agree with your analysis here, I don't think her family would've cared about his race.
With regard to the media interest - when reduced to the stereotypes that the tabloid news cycle reduces any character to, these two just hit every single square on the bingo card - rich, posh, beautiful, well connected Brit vs American, criminal, violent etc and it's an even better story for the tabloids because it's not a tale of two rich people or two poor people but two complete opposites and yes their race is another aspect of that.
Sadly I do think a lot of those stereotypes do fall into the horribly dangerous 'King Kong' kind of story I.e. violent black man with helpless beautiful white woman and I think it would be denialism to say there's not some interest in the fact that she's white and he's black. One of the first steps in tackling racism is pointing it out and describing it and I think people saying that this isn't at least a small part of the media interest are denying the racism that's built in to the society we live in.
I think where it will get really interesting if you're able to look past the 'they're monsters bring back hanging' POV is the what extent she was an active participant in what happened because that will completely upend the stereotypes of her being controlled by him/ him beig dominant and she submissive.
But we don't have the info for that yet and as I've said in previous posts... she has documented serious MH issues before ever having met him and he has convictions for violent sexual offences. I've gone into this in more detail before but you can guess where I am stood on what happened.