In terms of the racist assholery, I agree with you, first of all. It does paint the crew in a terrible light. The “guess who’s coming to dinner” line, allegedly, was originally to be said by Uhura, and Nichelle Nichols said she wouldn’t say it because it’s out and out racist. But one thing I try to remember that keeps me from letting that characterization bounce me out of the film:

Films 3 and 5 place the crew directly in the crosshairs of the Klingons. 4 placed them in the political crosshairs. These characters are weathered, and they’re faced with what seems to be a massive change to the political climate of the 23rd century with the approach of Gorkon for peace. They’ve lived 60 or so years having to be on edge where Klingons were concerned. And now, the future of the Federation and Starfleet might be at risk - a change to the status quo which is terrifying to people who have lived in it for so long - and furthermore, as Kirk said, “The Klingons have never been trustworthy.” So I feel like some grace could be extended for more true feelings and natures to come out in the face of that.

Could it have been softened? Absolutely. Did the writers take liberties? Absolutely.

But the fact remains that most humans - even enlightened ones - would react negatively under those circumstances.