I think most organ recipients would automatically assume their new organ was from someone of the same race as them. And in fact they’re reasonably likely to be correct, given that the donor registry match donors to recipients genetically, and you’re more likely to be genetically similar to someone of your same race than someone of a different race. (This is one reason why it’s far more difficult to find good matches for people of mixed race – there are fewer donors who have the same ethnic background, making it less likely that an available organ is a good match.)
I also think that most recipients would be willing to overlook any racist tendencies they may have in order to save their own life. Donors might not be so willing…
“In one case, for example, the family of a brain-dead Florida man agreed to donate his organs — but insisted that because of the man’s racist beliefs, the recipients must be white. Although the organs were allocated accordingly, Florida subsequently passed a law prohibiting patients or families from placing such restrictions on donation.” Source
Edited because I forgot to actually answer the question, haha! I’d accept an organ from anyone, no matter what their ethnic background, or anything else for that matter. Hell, I’d even accept an organ from a politician. ;)