I actually think that @Nevermore has the right of it here. The fact that sex between 'owners' and slaves is so common that the average slave is likely to appear mixed-race is likely to make the situation more acute. You have a society which, publically, extolls its strength as resulting from it's pure blood, yet there is a good possibility that a large percentage of that same population has heritage that is, less then 'pure' is going to instill a great cultural anxiety. Then add to that that the group that these quote, unquote 'superior' people rule over are harder and harder to differentiate just by looking at them. There is going to be a very real fear that some of the slaves could potentially pass and 'infiltrate' the nation.
I suspect that *American popular literature is full of taut thrillers about some major political or business figure really being a secret slave who is trying to undermine the country. Which is, of course, gag inducing from our point of view, but it sounds about right for DoD pulp fiction.
But it won’t translate well into daily politics as anything other than keeping baseborn people out of politics. Even in OTL under Segregation w interracial relationship was uncommon, Strom Thurmond fathered a child with a Black teenage maid and while it wasn’t public, it wasn’t a great secret either and no one used it against him. The only time we saw such accusations used against another politicians, were against McCain by Bush the Younger because he had adopted a Tamil child.
You have to remember that elite of TTL USA are depraved, amoral and hypocritical to a level, where anyone outside the system will find it completely incredible that no one react.