Race affects veganism because food and culture are often inextricably interlinked, and a rejection of one could certainly be construed as a rejection of the other. As I said, I'm white and not a vegan so I can't give an example pertinent to me and my life. So many ceremonies/practices inextricably linked to national/racial cultures involve food, and so many of those involve meat and other animal products. The people most likely to be defensive about those practices or ceremonies are those who feel like their way of life is at some sort of risk; minorities and marginalized populations, and rejection of those practices for dietary reasons could easily be construed by emotionally invested parties as a rejection of the racial/cultural identity in itself.
Imagine for instance that you are black, and your family are extremely invested in Kwanzaa. Now, upfront I will offer the caveat this isn't a great example, because I only know a little about it. But Kwanzaa was born from the struggle amongst the African-American community to assert themselves with pride and confidence, to resist ubiquitous oppression. Some people, particularly those who were deeply and actively involved in the civil rights struggle, could well be expected to take Kwanzaa pretty seriously. To them it might represent a time to be proud of the fight they fought, to annually reunite the family they wanted to have an equal opportunity in life. Now imagine the conflict that might arise from your not wanting to participate in a Kwanzaa feast because you don't want to eat or even be around the consumption of meat and animal products (chicken, fish, lots of creole food). That's certainly a legitimate personal choice to make, but surely you can see how that could be interpreted by some as a slight against the hard-fought African American struggle for equality.
This situation only arises from the historical oppression and marginalization of African Americans. A white person's family might be upset if their child doesn't want to attend Christmas or Thanksgiving and eat turkey, but racial identity doesn't form a part of it, because there's no real racial stake in them. Non-minority practices don't get conflated as representative of a racial identity as a whole. Nobody has family implying that 'you have to eat turkey at Thanksgiving because the meal is representative of us as a people'.
The Kwanzaa example is a bit hamfisted on my part; that particular feast doesn't hugely emphasize animal consumption; though non-vegan foods certainly predominate, specific recipes aren't singled out as being especially essential or significant. But many ceremonies and practices do have these sorts of codified meals that are imbued with significance in much the way that the Thanksgiving turkey is, and for people who experience racist discrimination, those rituals are often perceived as a very important part of staying resolute in the face of it. This is particularly pertinent to religious practices, like the passover seder for Jews, which is from what I understand very strictly codified in terms of what is consumed. Again, that isn't particularly my field. Perhaps someone to whom these issue is personally relevant can elaborate.
At any rate, I hope you can perhaps appreciate from this response that there are certainly times where racial/cultural identity and personal choices about consumption could have a great effect on each other and on a person's interpersonal relationships.