I think if you take the article completely 100% literally it sounds a little pompous and silly, but he still makes a very good point. The point is how by making us discard the little formalities and mannerisms, our dignity and manners can eventually be worn down and discarded entirely. Compare street pictures of London in 1913 vs 2013. You'll notice straight away that the people were far better dressed in 1913. Even young boys dressed better than 30 year old men today. Today people strut around in gym clothes(but in $100 versions, to sate their materialism).
I think this ties in closely with the author's point. People slowly relaxed their standards of dress, which people used to take very seriously, in favour of comfort. They replaced looking respectable with looking fashionable, and even looking fashionable is only for special occasions. People actually take pride in how slobby they are, I hear people on the internet joking constantly about how they throw off their pants the moment they get home and walk around in their underwear. The sheer lack of self-respect! We didn't go from all wearing suits to dressing like slobs overnight - it was a slow gradual relaxation of standards that led to this.
We see a similar effect in people's own homes, but compounded by the fact that women in the workforce has meant much less time and energy put to cleaning. The coffee saucer then, is a metaphor for the little things that may not matter much, but which if abandoned can set us down a slippery slope. A coffee saucer or the lack thereof does not make one dignified or undignified, of course not. But the point is that if you let those little things slip, if you decide to be lazy in how you dress, if you decide to leave those dishes in the sink overnight, if you decide you can leave the walls another year unpainted and the lawn another few weeks uncut - that's how you start off on the long but certain slippery slope to becoming a lazy worldly slob like so many people have today.
So no, a little coffee saucer isn't the most important thing in the world. It hardly matters at all. But its decline does represent a very important drop in standards among the general population.