Galvanic grounding, as normally practiced, is exclusive to low frequencies ("DC" as it were), and is only intended for safety -- providing a low resistance fault path to ground.
At RF, the impedance of all those wires adds up, both picking up ambient and wiring noise, and not really grounding your stuff (any RF ground currents your stuff produces, is dropped across that impedance, again generating voltages rather than sinking it to zero).
A more comprehensive grounding practice is required. Theory, perhaps.
It's not enough to run wires between points, that much is obvious. But what are you actually intending? You want a low impedance path, which separates a ground current from a signal current. You want a shield. A ground plane.
The ideal system, then, is one of shields -- Faraday cages -- which carry ground currents along their low-impedance surfaces. A shield has two surfaces: inside and outside. You want the ground currents to stay outside, and the signal currents to stay inside.
The Earth is conductive, and acts as ground. It's not ideal, because soil resistivity isn't very low. Suppose it were -- suppose you covered the ground with a continuous metal sheet so this becomes true. Then, anywhere you stick an antenna on top of this ground, its return (ground) current is sunk into the sheet, and spreads out over an area.
Ideally, you'd connect to the antenna at the underside of this ground sheet. Underground, as it were. This keeps the ground current on the outside, and the signal current on the inside.
That's not very convenient. But anything we construct, by a process of transforming the geometry, moving things around, without breaking the continuity of the ground/shield surface, will be identical to that situation.
Suppose, instead of routing the signal connection beneath the ground, we raise a bump, an emboss, on the metal ground. We run the signal inside this channel. Suppose we further raise and pinch this bump, so that it fully encloses the signal wire: now we have a coaxial cable, laying on top of (and still bonded to) the shield/ground surface.
Suppose we completely cut the coaxial cable away from the shield, so that it is only bonded to ground at the ends (at the antenna, and at the transmitter). As long as the cable is contiguous (full shield coverage over the inner conductor), it doesn't see anything different -- even though there is now a loop between shield, bond, cable, and bond, which can have EMF induced into it. The ground-loop current flows along the outside of the shield, leaving the signal undisturbed. (We can also reduce this ground-loop current by wrapping ferrite around the cable: the EMF drops across the ferrite instead.)
If we break the ground bond near the antenna, we have a big problem. Now the antenna's ground current must flow along the transmission line. The transmission line becomes a radiating element, and its orientation matters. Moreover, it brings ground current up very close to the transmitter. (The transmitter doesn't care, as long as the ground bonding is still good at that end. But anything on the antenna side of that bond, may be affected!)
Now, antennas don't all have ground currents. Good antennas are balanced, so that they produce very little (intentional) ground current. (There will always be some residual, though.) This is a more direct concern for unbalanced antennas, like 1/4 wave monopoles and such, which require a ground plane of some sort.
Suppose we leave the antenna-end ground bonded, and unbond the transmitter end. As long as the antenna bond is good, we won't have energy traveling back to the transmitter, along the shield. We will have ground-loop voltage (which may be ambient noise, or the transmitter's own output connection), though, which may affect the transmitter and connected equipment.
Now, to go from the imaginary to the practical:
Suppose we have an antenna tower, and a shack.
Ideally, the tower should be well grounded. It should be based deep enough into the Earth that earth acts like electrical (RF) ground. Any transmission lines coming down from the tower should be bonded to it, at the base.
The tower could also be installed on top of a large ground plane, or something equivalent to that, like an array of radials: wires laid on top of the ground, radiating away from the tower base, which serve the same purpose of shunting ground currents away. (Many monopoles, designed for insulated towers, or too short to use earth as ground, have radials in their design. They aren't so much monopoles as asymmetrical dipoles.)
Transmission lines coming up to the shack, should be grounded to the shack. The shack itself should be a Faraday cage, i.e., made of metal, so that the transmission lines are bonded to it on the outside, and only the signals penetrate inside the cage.
Inside the shack, we may again apply the same principle. The transmitter itself should be in a metal box: its output should be bonded to that box, and the cable simply connects from there, to the shack.
Indeed, we might optimize away the requirement that the shack itself be a cage, as long as the equipment within follows the same principles of shielding. This can be complicated to ensure, though: any box that has more than two connections, has more than two paths for ground currents (accidental or intentional) to flow away from it. You can very quickly get a complicated network, between mains (or whatever supplies your equipment runs from), various signal cables, audio cables, and etc., that accidentally contains ground loops that couple into the signal paths and cause problems.
Note that differential and balanced signals are no panacea. You might put the signal between two physically balanced wires, but you can't avoid the fact that the two wires act together, with respect to ground, or to the environment if nothing else. An exposed (unshielded) pair picks up 100% of the EMF around it, and that EMF will upset anything that's not prepared to handle it (e.g., a poorly made balun; an industrial RS-485 transceiver with its limited (usually ~12V) common mode range; an audio cable going to a solid state amplifier that tends to rectify RF on the inputs; etc.).
(Note that it's not enough to simply use shielded pairs; the shield must be bonded at each end, otherwise the break in shield allows 100% of that ambient EMF to enter the (common mode) signal path.)
Household ground is useless, because it's lengthy, not wide and contiguous. All these shields should, of course, be bonded galvanically, for safety purposes -- something that should happen naturally because you'll be connecting a lot of beefy shielded cables between everything -- but in addition, you need to set up the system so that there is a strong separation between signal currents inside the shield, and ground currents outside the shield. A properly wired system should not care if there's somehow a large RF voltage to Earth, because it's all within a Faraday cage that blocks any current that might flow as a result. The shielding must be solid and contiguous, at least at the circuit level (the equipment must be built so that ground currents flow around the active circuitry, while signal currents flow only to the active circuitry), but preferably (and often?) also the enclosure. The circuits or enclosures, then, are contiguous with the interconnecting cables, which are shielded. The interconnects can, in turn, be contiguous with the shack (if you choose to use / build a shielded shack), which is in turn contiguous with the transmission line(s) to the antenna/tower (which should be bonded to Earth).
Tim