I married a Brit. So I've pretty much stepped out of that expat bubble. Hence, I noticed this stereotype in the first place! You can't get to know someone better than marrying them, adopting in-laws as new family, etc
Sorry love, but that's utter bollocks. Getting to know someone and their family is not stepping out of the expat bubble. Sticking to a minute sample teaches you about the minute sample. Not the nation. Well, not without the sort of over enthusiastic extrapolation from teeny weeny samples that feeds sterotypes the world over.
I've had two husbands, lived with both of them in their countires, up to my eyeballs in their family and friends, for a quarter of a century. They don't pop our bubble. That's something we have to actively do for ourselves.
As long as you insulate yourself with a boundried circle of friends/warm aquaintences that by and large excludes host nation nationals, you are actively choosing to expat bubble yourself into a comfort zone that quite simply isn't equipped to challenge initial impressions and assumptions. It more often than not ends up being something of an echo chamber. Where sterotypes get reinforced via cherry picking evidence and fixed more firmly in place thanks to confirmation bias. One spouse + family is bugger all vaccination agaist that. At best they earn "exception to the sterotype" status.
When you pop your expat bubble, surprise of all surprises, one (extended) family and a light smattering of mates turns out not to have been enough to gain comprehension of the huge variety within "national characteristics/flaws". Most "national charateristics" ending up finally revealing themselves to be in need of mucho cherry picking of evidence to stay upright in the face of anything beyond the most superfical of observations. It does feel a bit 'duh! kind of obvious" post popping of bubble. But not so much beforehand.
You are entitled to have an opinion on anything. However it comes across as somewhat self important in an "oh we are soooo much more evolved!", expatty way to frame it as "challenging", be it the British class system, Spanish bullfighting, or the Indian caste system.
Rewrite your OP, with the same tone, for any issue in any country. It'll still read just like Sterotypical Brit Expat in Spain Person wrote it. Becuase it's not "challenging" issues. It's an exercise in pumping up one's daily quota of self satisfaction by contrasting oneself favourably with a faceless, homogenised mass of "the natives" who have been tidied away into a box called sterotypes in order to require minimum effort on the part of the person who is looking for a little covert "own halo" polishing. Possibly with a side serving of Rose Colored Glasses about the MotherLand.
What essential elements are required to sustain a class system and distract people into argy bargy between the classes with an emphasis on noticing their (alleged) differences rather than noticing their (very human) similarities ?
Stereotypes
Predjuice
Pejorative tone
Stoking one's sense of superiority at the expence of others
Given the tone and thrust of your OP, which contributed exactly the sort of ingredients that sustain a class system, whilst claiming to be "challenging" it, seems a touch contradictory.
Grabbing a cotton bud to deal first with the plank in one's own eye would seem a more genuine form of challenging.