Rejection really wouldn’t be a significant risk. Joint replacements, indwelling hardware ports, shunts, pacemakers, and many other devices are already in use without rejection risk. And you’ll note that very few of those interface between air and internal space. Anything that has exposed parts (ie a huge number of CBMs) is going to be much, much more at risk.
CBMs would largely not have been designed for the kind of use survivors put them through. Even industrial and milspec CBMs would assume the user has access to medicine now and again. Crawling through muddy swamp water and fighting a filth-soaked monster that bites you and claws at you, then going home and not being able to shower, is somewhat out of design specification.
Now, CBM definitely wouldn’t have taken off without accounting for this. Perhaps they’re made out of something like hormonal IUDs… They’ve got some sort of slow leeching antiseptic chemical cocktail impregnated in their coating plastic. Nevertheless, under standard cdda use, even if infections weren’t the norm, they’d be pretty common.