Oh for Christ's sake.Yes, it is, because there's absolutely no evidence [in] that scene to imply that her desire to be posted aboard the Enterprise was due to Spock's presence.But accusing a young human being who happens to be female of basing her life choices on less than pure logic? That's SEXIST!!!"
Yes, Sci, when you when you narrow everything down to that 15 second interaction, there's absolutely no evidence. If you ignore the entire rest of the fucking movie, if you feign ignorance of everything else that's revealed about these characters, if you convince yourself the turbolift scene and the transporter scenes happen in a vacuum with no basis in anything that's come before in these characters' history, if you are ignorant of the concept of "subtext" and simply accept everything presented to you at face value, and if you pretend to have no fucking clue about human nature... then, yes, you can argue there was absolutely no emotional component in Uhura's request.
Of course, your accusations of sexism would still be utterly baseless and personally insulting.
Even including the rest of the film, there is no evidence that Uhura's desire to serve aboard the Enterprise was motivated by anything other than her career goals. The Enterprise was consistently described by the other characters as being the starship you'd want to serve on, and Uhura's quoting of Spock's evaluations of her abilities (combined with her knowledge of the Romulan language) made it pretty clear that she's the most capable communications officer candidate and therefore deserves to be aboard the Enterprise.
No one's saying that she doesn't also want to be with Spock, but to argue that that was her primary reason for being aboard the ship when she herself made it clear in that scene that she wanted to be aboard for professional reasons -- and when the acting subtext was that of, "Why are you taking away what I've earned, asshole?" rather than, "Why aren't we serving together?" -- then there's absolutely nothing there to support the idea of her wanting the Enterprise because of him.