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.
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.