There are a number of distinct meanings to "class" as is true of a lot/most of words, and "style" is one of them. It can be fun to switch around the meanings in a debate, but word play like that is just wordplay.
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"...we are all the same" - in some ways that's true, in the most important ways in fact. But we are also divided, probably as much as we ever have been, between those who have the resources to control what happens, and those who don't. The markers change, and it's not just a matter of money (it never has been, wholly), but the divisions are still there, all around us.

We may all be in the same boat - but when it goes down, some people have places in the lifeboats and some have to sink or swim, and that's largely determined by "class". (And I don't mean class as style.)