I think I can answer my own question. The HDMI & coax signals are digital and the Bluetooth transmitter inputs, optical & RCA, are analog. So there is no compatibility. I could spend more per month for a cable box with digital & analog outputs and connect Bluetooth or connect Bluetooth to the TV, but operating the TV is an additional expense also.
which cable box and which bluetooth speakers brand and model is it?
The cable box is a minimal model from Comcast with only coax out & HDMI out for a TV that is rarely used. I was hoping to find a Bluetooth transmitter that would accept either of those inputs. This would allow my wife to listen to the Comcast music channels in different rooms or outside without having the TV turned on.
If we had makes and model numbers we could be specific
Optical is always digital.
A single RCA jack would be digital but two RCA (left and right) would be analog.
Digital audio output would be fixed level. Analog might be fixed or variable (check the cable box menu). This means you might not be able to use the TV remote to adjust volume.