Can you provide any evidence of this claim? A bandana can be any textile and certainly doesn't filter exhaled air. Being made largely of cotten and rarely washed, they also become virus spreaders if someone infected yet asymptomatic saturates a mask and proceeds to aerosol it around all day like a chum trail of plague.
Bandana is the worst option, especially compared to many vented masks actually use N95 filters preventing the inhalation of covid to begin with - and much more securely than your earloop equivalent