Ok, hear me out, yes, written Galician is understandable by any Spanish speaker, but spoken Galician can sound really alien to Spaniard. I never forget one day watching in the TV the street reporter interviewing someone and I thought they were foreign until I suddenly caught a word, they were a Galician speaking Spanish with heavy accent! No way I would be able to understand that person if they had actually spoken Galician 😅
As per the article information, yes, of course, Madrileños are despised everywhere in Spain, if you live somewhere where they are not despised, is because they haven’t visited yet… (As with any generalization, there are som wonderful people from Madrid, not ALL of them deserve to be despised, but the majority…)
If it is the splinter I assume that the joke is them complaining about a splinter while they had chopped down every single tree in the vicinity.