Hi,
I'd have them stack. The Gift gives you a penalty and causes people to have a negative opinion about you. That negative opinion remains, but the penalties are offset and even reversed.
I like to think of the social effects of the Gift combined with great social skills akin to being a particularly charismatic person of color in the antebellum South*, or an obvious but charismatic Jew in most times and places.
*EDIT: Or maybe in America today, with the antebellum South being akin to a Blatant Gift. I'm not trying to be (and am not equipped to be) precise about the trajectory and state of racism in America.
Anyway,
Ken