Gates carbon drive on carbon frame
There is no reason a carbon fiber composite frame could not be built to accommodate a Gates drive. CFC can be bonded to a metal split dropout no problem.

CFC frames designed for Gates drives are likely not common because the frame materials and drives are intended for different niches. CFC frames are intended to be light, efficient and fast, are relatively expensive compared to other frame materials and are combined with derailleur drivetrains. Gates drives require internally geared hubs which are a bit heavy and are aimed at 'practical' cycling offering no mess and low maintenance, where CFC frames are not used as alloy frames are perfectly adequate.