A bit like the time when Nintendo told us that Yoshi is not a dinosaur, only to be disproved by its own resources, the company is happy to play fast and loose with 'lore' around its more light-hearted characters. Why not, too, as there are bigger things to worry about.
Still, in a fun / random occurrence, an updated character profile for Mario on Nintendo's website apparently says he's no longer a plumber, with those days in his past. The translation is via Kotaku:
All around sporty, whether it’s tennis or baseball, soccer or car racing, he [Mario] does everything cool. As a matter of fact, he also seems to have worked as a plumber a long time ago...
This does make sense, as Mario stopped having a 'profession' pretty early on (when you think about it). He may have showed off some plumbing skills in Super Mario 3D World, but that doesn't mean it's still a job.
Or maybe this is overthinking things...
With thanks to SLIGEACH_EIRE for the heads up.