With being white it’s not so clear here. Being white doesn’t definitionally come with clear net privilege because it’s such a diverse group: your life is likely much better than some devestatingly poor white person in Appalachia, or even just the majority of white people if you work in tech.
As a test for privilege, ask yourself: “would I trade places with a random white person and accept these racist comments”? Is that a “good deal” like with the rich person example? It’s not clear and probably not worth the risk you end up trading places with the many white people in crappier circumstances than you. That’s exactly the proof: many many white people don’t have so much privilege that you’d happily trade places and take all the racist comments too. In other words: it’s really NOT punching up in many many of the circumstances, many of the white readers who see your comment, it is just exactly punching down for them.
Not that the above should even have to be argued, being racist isn’t ok even if it’s punching up, just as sexism against rich women isn’t ok, or homophobia targeting rich gay men. Jewish people are exceedingly successful as a group along dimensions like income and wealth, so it’d be “punching up” in some sense, but does that justify antisemetism? Of course not. Trying to justify racism with “it’s punching up” just comes across as “I want to be racist but don’t want to be seen as a racist”.
We’re smart enough to convey our viewpoints without having to insult. It only helps with our righteous self-indignation at the expense of making inroads towards actual, positive change.