You mean like Tax cuts.
Now I am confused. If the Republican base is suppose to be so stupid how are they suppose to pick up on the subtly that tax cuts means anti-black?
EDIT: Or you know you could point out which parts of the Republican platform YOU personally feel are racist?
The argument, whether you proscribe to it or not, doesn't rely on everyone 'getting' why they agree so strongly with a position. In some cases, maybe many cases, it can simply be long-simmering resentment at blacks for perceived injustices in life (didn't get into the school this person wanted 'because of affirmative action,' poor because 'blacks take welfare money and so his taxes,' whatever other justifications some people make to blame their troubles on others) that then fits with what the dog whistle is implying. If you're angry at the "welfare queens" eating up your taxes, and your image of a "welfare queen" has always been a single black woman buying nice things and fancy foods (or junky foods) with food stamps, then whether or not you see "food stamp president" as race baiting, it fits with racist parts of your overall worldview and you'll respond more powerfully to that phrase.
There are long-standing stereotypes and archetypes for black people. Angry black man; magical negro, playing off of how 'exotic' and 'other' they are; lazy and unscrupulous; stupid and beastly, which actually has ties to decades of then-respected scientific 'race theory' that was taken very seriously by nearly everyone, especially during the eugenics era. You can see these stereotypes in the words that some liberals argue are code-words for "black guy in power." 'Angry' fits the first one; all the 'European model,' 'born in Kenya,' not a 'real American' stuff fits the second one; Michelle Obama as a 'wookie' or 'gorilla' or calling her 'fat' and mocking the healthy eating stuff ties into the last two. Worrying about an "unfathomable darkness" falling over the country is pretty obvious, if you're looking from this perspective.
It's kind of like how poll taxes and literacy tests are perfectly defensible things to propose in some ways, but were used to enforce the racist system that created them. Defenders could say "but how can they be expected to vote well when they don't have a stake in the system by paying taxes? How can we trust them to vote well if they're not even literate? We're not being racist!" But of course that's exactly what was intended.
You don't have to agree with any of these arguments, but at least make a good faith effort to understand the perspective and history behind them.