The GOP appeals to the white working class not through class issues, but through racism. Because the white working class in the United States is, by and large, racist.
There's definitely a Horseshoe Effect when it comes to the racial politics between wealthy white Republicans and white working class Republicans. It's arguably their biggest common ground.
It's not that the white working class doesn't care about being underpaid and exploited for their labor. It's not that they're unaware of how much bosses and the capitalist system screw them over. On the contrary, they're quite cognizant of those issues. It's just that they are much more fearful of competing with immigrants over jobs or minorities fighting for racial equality, and they vote accordingly.
Some anecdotal evidence on my part: I'm a white woman born and raised in the South where my mom, dad, and stepdad's sides are all economically diverse but solidly Republican. I've heard pretty much every racist talking point across this large class gamut that doesn't include overt, KKK racism. A very close family member, a woman who grew up working class (and became middle class by marriage), cited the aforementioned fear of immigrants and minorities on why she voted for Trump, more than any other issue. The white working class kids I went to school with were also solidly Republican, and you bet your ass they had racist views!
There's a popular narrative that the white working class started voting Republican because the Democratic Party abandoned class issues. That narrative implies that the Republican Party has made class issues a large part of their platform, but that couldn't be further from the truth, as their embrace of Trickle Down Economics proves. Instead, the Democratic Party started emphasizing racial equality, which turned off the white working class by and large.
There's another popular but just as inaccurate narrative that the white working class are voting against their interests. From a class perspective, that's true. But once again, the white working class greatly prioritizes their racial politics over their class politics, so in reality, they actually are voting for their interests. Maintaining white supremacy - whether they want to admit it or not - interests them more than addressing wealth inequality.
As long as all of these factors hold true, the Republican Party will continue to court the white working class vote with Race Panic ad infinitum.