@Briannaco
Of course it's more offensive to say to someone "you're ao working class" or "you're so poor" or "you're rough"
Then it is to call someone "posh".
Its nastier to insult someone who has very little than it is to insult someone who has a lot.
But calling someone "posh" is so often not based on what they have. As many on this thread have pointed out, accent seems to be a big factor. It's particularly unpleasant when it's othering the person who just wants to get on with everyone. Your theory only works if it's someone with privilege and resources being jeered at by those without, driven by unfairness at the situation. It doesn't stack up when the so-called "posh" person doesn't have these things - then it's just bullying the person who's different/in the minority.
As someone with a SE accent I am perceived as "posh" where I live now, and have been in other places. Fortunately here people seem to quietly assume I'm posh but still interact with me based on whether I'm a nice person.
Unfortunately when I was very young and very vulnerable I experienced the worst of being "othered" due to my accent (in a different area) - I needed help from mental health and homelessness services, but was perceived as privileged/wealthy (whilst living in extreme poverty), so couldn't possibly have any real problems and should just pay my way out (with money I didn't actually have). The most stark example of this was being told I should probably be in psych hospital for a bit, and my parents should pay for me to go to the Priory. A psych nurse actually said that!! (This was about 20 years ago).
That was an area particularly hostile to anyone not "local". When I moved areas I was scared to speak in public, I remember cringing as I had to ask some builders directions and being amazed they just told me in a polite and friendly way.
Anyway, the whole thing of it being ok to take the piss out of the "privileged" group only works when you are looking at large groups as a whole, where one clearly has more resources. It doesn't make sense if its brought down to the individual level when that individual has fewer resources than those alienating them.