The NEC is fairly clear about wiring like coax, network, phone, they all classify as low voltage wiring . The rules are that anything connecting to the home from the street has to have some way of equalizing the ground potential difference between the home and the last ground point . Coax coming from cable companies is supposed to go through a ground block at the home, this is NOT for lightning protection, it is for equalizing any potential difference. Without a grounding block in place a ground inside the cable box on the street and the ground of a connected device in the home would differ, that causes current to flow from ground A to ground B and that is what the NEC is trying to prevent.
If you are running coax out one wall and into another room you do not have to use a grounding block because there is no difference in ground being created. The same rules apply for CATX cables, run it all you like outside the home , but if the cable connects two independent structures you have to use some sort of grounding between the two structures, from one room to another in the same home is a non issue as far as the NEC is concerned.