Comment by rz2k

I am suspicious of any claims about relative cleanliness. As with wooden vs plastic cutting boards, our intuitions are likely misleading.

To be an effective fomite the currency has to not kill the microbe, and it has to readily give up the microbe to the next recipient. Organic materials like cotton or linen seem more likely to simply absorb a viral envelope or bacterial cell wall, thereby rendering it ineffective. Furthermore, the porous nature makes it more difficult for the note to give up any microbe that isn't immediately killed before it naturally dies over time.

A brief search of the scientific literature doesn't seem to show any conclusive results, but it does seem like the relative performance is pathogen specific.