Given that defining class is entirely and inherently arbitrary in nature, it means your premise is no more valid than an American that chooses to define themselves on class by income.
I'm talking about social class, which is a very real and well-documented phenomenon. Money is not a very good predictor of social class, because it only controls what you can buy.
To belong to a higher class, you have to use your money to buy the props that are necessary to perform that higher class, and you have to be able to do the performance as well.
For example: You buy business class tickets for your entire family for a vacation in Europe, and you still complain about how horrible flying is. Congratulations, you just performed upper-middle class!
TV labor-economics is a special category composed exclusively of hand-waving that lets the writers portray cool stuff without having to actually use nothing but the idle rich as characters.
In the UK on the other hand, a lot of our characters seem to be from working class backgrounds with a lot of money troubles and lower key living conditions. Like say, basically anyone from a UK soap opera (like Eastenders or Coronation Street). Or the main characters from Only Fools and Houses or Steptoe and Son.
He's a nuclear safety inspector; does that count as blue-collar? I don't really know much about the job frankly. I don't think it's implausible that it may be quite enough to support a family, especially in a small town.
Not to defend the realism of the Simpsons wrt his job, but I'm pretty sure the joke is that he manages to keep his well-paid, relatively important job.
I wouldn't consider either of these things something to proudly stick to.
> Here in the US I've heard families earning from $30k to $200k, working jobs from manual labor to white collar, call themselves "middle class."
Sounds perfectly reasonable to me. Where I'm from, the most important marker for middle class is that you value education very highly, and that you don't value physical labour above any kind of work.
Obviously, the people in your example at the low end of the pay scale would most likely be lower middle class, and those at the upper would be upper middle class. The major distinctions between those would be how to perform social interactions and the size of their social networks, but they all agree that life's goal is to send your kids through college.
(As opposed to being working class which means you do not value education highly, and you value physical labour ("real work!") higher than any other kind of work.)