I think it's the responsibility of the white fisherman in your story to read the parts of the text and listen to the parts of the arguments that address him and his problems (and there are plenty), and to be glad that it also helps minorities. His failure to figure that out is his fault, not the people trying to help's fault (I'm not great at softening my tone, you may notice; I'm genuinely sorry about that).
So it's pretty unrealistic to expect every fisherman to go out and read every bill that comes before Congress. Members of Congress don't even read the bills.
It's supposed to be the role of journalists to convey what the bills do to the public. And then that's what we're talking about.
If the media is telling everyone that the bill is to help someone else and not you (with the plausible implication that it could come at your expense in a zero sum game), it can't be that surprising that this gets less support than putting more emphasis on the fact that it also helps you.
I think this is missing the problem with that framing.
You're kind of assuming that the reason people oppose a bill purported to solve a problem for minorities is that they hate black people and want them to be miserable.
Suppose you're a white fisherman just scraping by on the Gulf Coast. Things are bad. You wish something would change.
The media reports there is a bill being debated in Congress. It's a thousand pages long and you don't understand it, but they say its purpose is to help black people. Gosh, you wish they would do something that would help you for once. Probably going to raise your taxes to pay for it, too. This bill sucks.
Compare this to saying that the bill is to help working class people. Hey, working class, that's you! Finally!
It's the same bill. It helps black people because they're disproportionately working class. To specifically tell other working class people that it's only meant to help someone else is how you destroy solidarity. It's what you do if you want them to fight each other even though they have a shared interest.