OLIVER: Now, I'm not saying that all Larrabees have been saints. There was a Thomas Larrabee who was hung for piracy, and there was a Benjamin Larrabee who was a slave trader, and there was my great-great uncle, Joshua Larrabee, who was shot in Indiana while attempting to rob a train, but there never was a Larrabee who behaved as David Larrabee has behaved here tonight!
DAVID: And exactly what have I done?
What David has done is to betray his class by daring to fall in love with a chaffeur's daughter. Oliver is a hyperbolic caricature of class snobbery; piracy, slavery, robbery—all those are forgivable. But breaking class barriers is beyond the pale.
SABRINA: Just imagine, you press a button and factories go up, or you pick up a telephone and a hundred tankers set out for Persia, or you switch on the dictaphone and say, "Buy all of Cleveland and move it to Pittsburgh."
Sabrina fancifully describes Linus' vast wealth and power. That power is fun, and also exciting and exotic, what with the tankers whooshing off to Persia. The attraction of the Cinderella story isn't just true love, but true love wrapped in incredible material comfort and high status. That's part of the attraction of Sabrina as well.
THOMAS: I like to think of life as a limousine. Though we are all riding together, we must remember our places. There's a front seat and a back seat and a window in between.
LINUS: Fairchild, I never realized it before, but you're a terrible snob.
THOMAS: Yes, sir.
Sabrina is about how class distinctions don't matter. It's very careful not to ever suggest that rich people are bad, or that rich people exploit or have too much power over poor people.
So it's not Linus who's the snob who think the classes should be separate; it's Thomas. The chauffeur wants everyone to stay in their place—which allows Linus to appear as the voice of enlightenment and democracy. Remember that Linus' estate in real life was the estate of one of the film's producers; Hollywood is funded by rich people. Hollywood loves rich people; it doesn't want to make them look bad.
SABRINA: Kiss me, David.
DAVID: Love to, Sabrina. [kisses her]
SABRINA: Again. That's better.
DAVID: What's the matter, darling? You're not worried about us, are you? Because I'm not. So there'll be a big stink in the family. So who cares?
SABRINA: David... I don't think I'm going to have dinner with Linus. I don't wanna go out with him.
DAVID: [chuckling] Why not?
SABRINA: I want to be near you.
DAVID: Oh, I know how you feel, Sabrina. It must be an awful bore, but if Linus wants to take you out, let's be nice about it. It's very important. He's our only ally. Don't you see, Father will try to cut off my allowance and send me off to Larrabee Copper in Butte, Montana, and we don't wanna go to Butte, Montana, do we?
Sabrina wants to stop seeing Linus—but she can't because he has power, not only over her, but over David. Sabrina is falling in love with Linus, but she's also stuck with him because he has money and influence, which she and David can't ignore. Sabrina's fantasy is that social class doesn't matter to love—but at the same time, as this quote points out, class and power sneak into everything.
THOMAS: Democracy can be a wickedly unfair thing, Sabrina. Nobody poor was ever called democratic for marrying somebody rich.
Thomas is pointing out that the rich are seen as virtuous or egalitarian when they marry the poor. The poor, on the other hand, are seen as trying to get ahead when they marry the rich. Even equality favors the rich—which, as Thomas says, is "wickedly unfair."