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.