Haus Schuhe or slippers as you might know them

I first came across Haus Schuhe when the children started school here, it was on the list of things they had to have at school, a pair of slippers.

At Kindergarten and Grundschule (primary or first school) I guess the theory goes that the children spend break time outside getting shoes muddy and wet and then come into the classroom shedding all this dirt over the floor which they often then sit on. Consequently at this level of schooling the children all need slippers in school to wear in class. Fine.

Ben's now at Gymnasium (high school) and although they spend break times getting dirty they don't then come into the class and sit on the floor in their dirt, so no Haus Schuhe required.

The slipper selection in shoe shops is huge, clearly to supply all the school kids from the age of 3 to 10 but also for the adults.
You see Haus Schuhe are very popular as home wear here. Most Germans within the sanctity of their own home will wear some unattractive rubber soled constructions, they often look a bit Birkenstock-y, I've even heard it said that no German would be seen dead outside of their house wearing Birkenstocks as they consider them to be Haus Schuhe and not Schuhe clearly! Whereas I would previously rarely let a summer go by without investing in a new pair of Birks to get the air to my piggies, not so speedy now that I live in Germany though - don't want to give them any excuse for sneering at me, thinking that I've absent-mindedly come outside in my slippers.

And it gets worse! When visiting someone's house they often have a basket of felt, guest Haus Schuhe, because clearly they don't want you to wear your dirty shoes and track mud and germs all over their antiseptically clean wooden floors, but at the same time they don't want you to catch a chill through your stockinged feet whilst enjoying their hospitality, so they expect you to wear some felt things that countless other visitors have worn on their stinky feet.

NO!
It's so not happening! I'm more than happy to remove whichever pair of shoes I've chosen to go with the outfit I'm wearing (which quite probably complete said outfit and without them the outfit will look a little less perfect) but to then wear a pair of grebby felt things?

NO! And no again. I'd rather get cold feet, although I would of course not tell them that, I'd say instead that I have incredibly hot feet that don't feel the cold!

Can you even catch a chill through your feet?