It is possible to apply an antibacterial coating to cotton fabric using a combination of chitosan and graphene oxide, where chitosan provides inherent antimicrobial properties and graphene oxide enhances the coating's effectiveness against various bacteria. The combination of these two materials can effectively impart antibacterial characteristics to textiles while maintaining their structural integrity.
You can certainly do that, but I would be careful about applying unselected graphene oxide to something that is simultaneously exposed to wear and close to inhalation organs. Graphene oxide, depending on the flake size, may have chemical functionality that enables DNA interaction and you don't want to inhale that.
the question would be, what do you consinders as anti bacterial? Chitosan has some bacteriostatic effects, it reduces the growth. GO also. Both can be easily coated to Cotton. If the strength is drecerased depends on the coating conditions. An increas in tensile strenght you would not obtain,