Why Christina dismisses Hilary?

I agree and it's one of the problems with the film. Her housekeeper behaves in a hostile and ignorant way yet Christina ignores it.

It was a definite workplace violation, though, if you think about it -- she went to her boss's house to find out about her boss's daughter's interracial relationship -- none of her business at all -- and when asked "What brings you all the way over here, Hillary?" she makes up a random excuse, and Christina says "Couldn't you have called me to tell me that, Hillary?"

And also before that Hillary has a very condescending, sarcastic tone toward Christina saying her daughter "has been telling me a congratulations is in order and you didn't even know" -- her tone when she says it and her facial expression and frown are as if some absolute atrocity has been committed. When she says "I wish you every happiness" that tone and half-smile(/half-frown) with teeth seem so artificial it's like she's holding back what she really wants to say.

In my opinion Christina had every right to be upset and also feel like it was a strong workplace violation, and her comments to Hillary, I thought, were also meant to be funny to the viewer for their bluntness (they were funny to me): "It's not that I can't stand you, Hillary, even though I can't, it's just you and I have a different way of seeing things" and "Take out anything that could subsequently remind me of you including that bizarre 'kinetic sculpture' thing you have such a fascination for." And you have to admit, that so-called "sculpture" we saw earlier on was pretty dang random and weird.

There was nothing respectful about Hilary's actions or words. Christina most likely knew that Hilary was a bigot, but it had never flopped over in to their personal lives. This time her behavior was personal, and could no longer be tolerated.

Christina acknowledged Hilary's contributions to the job, and compensated her for that. But she wouldn't work with her anymore.

Hilary went out of her way to snoop and make not so subtle comments about the situation. Imagine how she would have behaved in the future.

I think the point that was trying to be made by this character was that racism comes in many forms. Most obviously is the most overt and harmful form down in the South of Jim Crow, which had been on everyone's mind in the preceding decade as the Civil Rights Movement played out. But perhaps the filmmakers (Kramer, the screenwriter, I don't know who) were trying to convey the point that racism was not confined to the South and that even in a supposedly liberal place like San Francisco, you would find less overt, but still quite odious racism, a very hypocritical form (and the South was never hypocritical about its racism). So Hillary's attitudes are quite restrained, but entirely obvious nonetheless.

I grew up in San Francisco in the 60's and 70's, but my father came from Hawaii (moving to SF for college). My father recounts that once in the 1960's his cousin from Hawaii (who was part Hawaiian, so somewhat dark, especially with a suntan) came for a visit, and my father brought him along to one of the big athletic clubs in SF (I'll omit which one). Another older member pulled my father aside and with evident surprise and consternation asked him why he had brought a "black" to the club.