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I'm a caucasian man with an Asian-American girlfriend; to make me even more evil, she's the youngest in her family (her mother still refers to my GF as "her little baby", even at 38). What worked for us probably directly won't for you; two of her sisters got married, one to a caucasian man and the other to a Chinese-American man. The former is terribly obnoxious; the latter is downright rude and insulting to my GF's parents, and abusive (physically and emotionally) to my GF's sister. I've always tried to be respectful, patient, inobtrusive & listen more than talk when visiting, to dispel the image of overbearing whites who just want to hear themselves talk. Over the years they've come to accept me, even like me. It shocked my GF when her father sat down with me after a meal and we talked about family, cooking (one of our mutual loves), travel, and all sorts of smalltalk that makes you feel at home. It does help that we all have great similarities in family backgrounds; 6 kids in both our families, mine were immigrants from Italy, and great big family gatherings where enough food was made to feed a small country.
The best "tactic" was that, really; to concentrate on the similarities. We're not all that different. We sometimes let ourselves believe that isn't true, and there's enough folks who want it to be true, but that doesn't mean I have to buy it lock, stock & barrel.
(It probably helped that my GF's father always considered Italians & Italian culture exotic & cool... fetishization can go both ways).
But... it still took many years. We celebrate our 17th year together in a few weeks, and to be honest I've only truly felt welcome for the last 5-6 years.
Best of luck to you both.