What’s the deal with the blue cotton shirts that people wear in Schwingen? Every man in my family seems to own one.

Dear anon, before all, thanks for your question.

These kind of shirt are armaillis/Senner traditional shirts, and by extension became a sort of uniform for Swiss farmers.

https://youtu.be/skpNG4myJw4

They’re available almost everywhere, from tourist traps for a huge lump of money to Landi supermarket for about CHF 25.-

On the reason all the men of your family are wearing the armailli’s shirt :
a. they’re Swiss farmers ;
b. they like Swiss traditions (and may practice competitive Swiss wrestling/ shooting/fondue eating/Hornussen/Steinstossen, among other sports) ;
c. they like traditional, no nonsense, solid garments for work and/or sport ;
d. they are leaning politically toward UDC/SVP ;
e. they misunderstood and are quite enthralled that famous italian designer Giorgio Armailli made a very Swiss collection for this winter ;
f. some or all the above.

(I’m b. & c., tag yourself) #ranzdesvaches

Hoping I have been of some help in your questioning.