I can see why you asked this hypothetical since it would take supernatural intervention for Haley to win a Republican primary.
Uh, citation needed.
She's relatively moderate and a woman of color.
She’s really not “moderate,” and her conservative views make the fact that she’s a “woman of color” irrelevant ... though I know you prefer to believe otherwise.
People perceive her to be moderate, which is the problem.
And yes, of course her being a woman of color matters. The GOP primary base is too racist and sexist to vote for her.
The GOP primary base would have pissed themselves happy to vote for Palin, and plenty of other Tea Partiers and evangelicals in the Republican base (Keyes, Bachmann, Cain, Fiorina, hell even Carson was polling even with Trump at one point) were female/nonwhite
All of those people did poorly in the primaries.
Palin was/is beloved by the Tea party masses. Were Republican voters "too sexist" to vote for her when she was on McCain's ticket?
I don't know why "doing well in the primaries" is the only criterion that matters to you, since all of those people I mention were heavily endorsed by the Tea party faction (which is the most socially right-wing faction of the GOP) and were polling competitively and/or leading the pack at one point or another
Republicans voters care about getting their agenda passed one way or the other, so if Haley is the nominee, yeah, they'd vote for her. If she loses, it's because she's ideologically out of touch with the Republican party (which she is), not because she's a "woman of color"