I think it comes down to your level of analysis, or how you define relations. Having been living off $30-40k income for most of my life, I can definitely get the sentiment of the large differences between that and someone making $100k (even $60k), or at least someone living a working class vs middle class lifestyle. But that also goes for someone making $0-10k to $30-40k. Either way, the salience of financial insecurity hits a lot harder for someone with less existing cash.
That said, I also get the sentiment of the nil difference between working and middle class versus the ultra rich who generate huge swaths of passive income and can basically can dictate whether or not the lower classes have enough for rent. Why bother fight against each other when there’s a much larger and casual target.
In a more nuanced answer, for solidarity sake we do need to recognize our similarities to work together for a better system. But that doesn’t mean we should ignore our differences and privileges either. We should work towards achieving core necessities for all even at the cost of our own privileges (i.e. an opposite tragedy of the commons: those with some threshold excess contribute to the pond). Determining that threshold is another question, with both absolute and relative poverty thresholds with their own criticisms. And not to say that no class hierarchies will form either, technically skilled and heavily laborious jobs should be rewarded, and people will always try to skim a little off the top to get ahead of their own benefit. But in recognizing our differences, we recognize a need to monitor ourselves for the benefit of everyone.