Here in the UK people will cling to being part of their class as though their life depends on it.
Middle class people had rather die than be called 'working class'. The working class hates the middle class with an intense passion, thinking they all eat kale, basically live at Starbucks and try to turn England into a communist utopia.
Class divisions just play into the hands of the one and only class that's different from the people who work for money: Those who do not have to.
If society was nicely split into "those who work for money and those who do not", I believe it would very quickly become clear who is acting in whose interest.
But so long as the veil of "working vs. middle, vs. upper middle" shrouds our collective ability to see who is truly ruining it for everyone, nothing will change.