I wonder which part of this (admittedly odd fashion statement) seemed surprising to you? Gas masks were of course ubiquitous during the war, so this was probably only about as eccentric as wearing an N95 mask would seem now. And the alarm clock seems like a fairly practical if whimsical hack in an age when chronometers would have been mechanical, and therefore quite expensive.
I feel like the average person absolutely was not wearing a gas mask at all times. Having myself used an N95 in my neverending war on pollen I totally understand though.
No, of course people didn't routinely wear them. But every citizen was issued one. Children took them to school every day, and were drilled in their use.
It's still an eccentric thing to do, of course. But, like the alarm clock tied around his waist, it was an instance of solving a problem by grabbing something close to hand.
I bought one at a swap meet in Amsterdam a few years ago. They were piled up high and cheap. It made a fun gift for a friend back home, but we got really odd looks on the train when wearing it :).