The note seem to resemble the real-life Journey series $20 (https://en.wikipedia.org/wiki/Canadian_Journey_Series), which were cotton paper, and were printed until late 2012/early 2013.

In-game, The Collapse (http://thelongdark.wikia.com/wiki/The_Collapse) happened in late 2012 (with Milton Credit Union closing in September 2012), so the polymer notes (if they were made) probably never reached Milton.