Lanyards, strings used for holding name cards, often has the shape of a Mobius band.

A picture of lanyard: Many more can be found on Google Image.

The purpose of using this shape is probably to help the card stay flat on the chest.

This is certainly a real world application of the Mobius band. It is a bit amusing to see so many people wearing an unorientable, one-sided surface! Showing a lanyard and pointed out its shape can be a convenient way to introduce the Mobius band to people.

(I learned this from someone else. A search on the web shows that somebody has noticed this earlier: [https://www.reddit.com/r/AskReddit/comments/l890m/why_the_hell_are_keybadge_lanyards_made_into_a/])