I need people to understand that pointing out Lucifer's microaggressions against sinners, and Alastor specifically, isn't claiming he's racist.
Of course Lucifer is not racist. He's not human, sinners on that front are all equal to him, but what they are in his eyes is "equal worthless garbage".
He's a classist that has formed a cast system by creating the Ars Goetia and putting them as the noble class, while the other hellborns are either normal citizens, a part of them treated like the exploitable working force (imps, Satan admitted to have created them to be obedient) or straight up animals and pets (hellhounds). The social structure is clearly established in Helluva Boss and it is also a source of conflict.
Obviously Lucifer needling Alastor, especially when Alastor fights back or starts pestering Lucifer himself, is not him being racist.
But can we start looking at it from Alastor's perspective?
Lucifer, King of Hell, being at the top of the food chain, from Alastor's pov is a pompous literally-white not-man that had everything handled to him on a silver platter and lives off a privileged lifestyle, while he looks down on sinners and, on top of that, he's also a neglectful parent that has just recently started to try, and he's failing miserably.
Lucifer's insults towards Alastor are a bit too deliberate to be a coincidence: bellhop, the hired help. Mr. Useless. Alastor corrects him everytime, and Lucifer keeps insulting him that way because he doesn't like him.
Again, Lucifer is not racist, that's not the intention. But maybe let's consider that Alastor lived during the first decades of the 20th century, because he did, and the visuals from s2e4 weren't subtle; Alastor experienced racism. Alastor knows how racism looks like: he lived it.
How do you think Lucifer's behaviour looks like, when Alastor knows Lucifer hates sinners and he acts just like the rich white men he had to deal with in life?
The fandom is so very quick to dismiss the characters' background, but Alastor's gets dismissed even more easily.
In the end, what Alastor can't stand is disrespect.
Logically, Alastor would know Lucifer is not calling him the bellhop because Alastor is mixed, but Lucifer's still classist, and why should Alastor give him any grace? Lucifer doesn't deserve Alastor to cut him some slack on the matter, just like Lucifer doesn't have to like Alastor or have him in his room. It's the way Lucifer attacks him that matters, not that he's attacking him.
Alastor and Vaggie don't get along either, but Vaggie doesn't get under Alastor's skin because her assessment of him is not wrong, and doesn't dismiss him or dimminish his role in the hotel. She's annoyed by his antics, not that he's a sinner existing in her proximity.
Lucifer has a lot of prejudice against sinners, and he's right now incapable of viewing even the ones at the hotel as people trying to get better or worthy of being remembered. Alastor has all the reasons to draw comparisons between the disrespect he received in life for something he couldn't change and the insults Lucifer throws at him, because the sources are not too dissimilar at their core.
It's something humans do subconsciously and, I know this sounds crazy for some, but Alastor is human like the others. Even if he hates to show it.