In short
White radomes are common in many applications, this is the logical choice, a white material reflects sun radiations which otherwise introduce electronic noise in the antenna.
Black radomes, only found in fast moving vehicles, owe their color to antistatic carbon powder used to eliminate electrostatic charges created by air friction. The replacement of black radomes by gray radomes is to hide radomes by lowering the sky/radome contrast.
The appearance of white radomes for aircraft is due to the fact satisfying white coatings have been found, they are used because they provide a better radiation protection than gray radomes. White conductive radomes combine all advantages but are more difficult to produce, and likely useful only for most sensitive radars.
On this aircraft, white radomes are found for the nose (radar), at the tips of the vertical stabilizers (VHF) and on top of the fuselage (satcom).
Constraints on materials
Materials for aircraft radomes must be resistant like other aircraft parts (pressure, heat, rain erosion) and must be electrically conductive to carry static charges, without significantly affecting waves to/from the antenna they protect. Coatings using conductive oxyds based pigments must be engineered in a way they appear like air to the antenna in the band of frequencies used, in order to not modify waves characteristics. This is possible but difficult as UV and rain make them instable. The stable ones are likely limited to the ones we see in use.
White / low noise is the best option for fixed installations
For fixed stations not degrading the antenna efficiency is most often the main concern and fixed radomes are white.

Sea-Based X-Band Radar, source
White reflects a large band of radiations from infrared to UV, both having negative effects.
IR is heat which can be eliminated by cooling, this makes the system more complex but is easily feasible. IR also creates additional noise both in the radome material and in the antenna. This reduces the radar performance. This effect cannot be offset, and when performance is critical, the only way is to reflect radiations to prevent them entering the radome.
UV degrade the material and change its dielectric properties.
Black is a better option for static charges elimination
Airborne radomes, specially at the nose, suffer another problem. At high airspeed, air friction ionizes the outer material. Charges accumulate if the material is not conductive and the radome becomes opaque to waves.
Metals are the best conductors, but they also block waves. Conductive radome materials or coatings are actually made of black carbon powder. This is the color we see since radomes are usually not painted to minimize signal losses.

F-16A Block 1, source
Black is not the best option for radio noise, but has been necessary at a time to eliminate the more problematic static charges.
Gray is a good compromise for visibility and static charges
Black was found to have a significant drawback for a fighter: It increases the contrast over a clear sky, making the aircraft more visible. Conductive gray materials partially solve both the noise and visibility problems. From this page:
Because the black radome made the aircraft look like small black dots on white paper, the subsequent batches of F-16 switched to gray radomes.
The material could be a conductive black material receiving a very thin layer of gray coating specially crafted for the wavelengths used. Or the material could be gray and also conductive.

F-16AM Fighting Falcon, source: airplane-picture.net
Antistatic white radomes are better than gray for noise
Many antistatic coatings do not retain their properties under erosion from rain at high velocity and heat from friction. Their conductivity increases with time, affecting waves transmission. Stable white coatings are available, e.g. this white antistatic topcoat:
offering static charge dissipation capability and color tailorability as well as radar transmission consistent with current radome coating requirements.
They solve the visibility and electrostatic charges problems of military aircraft which was already covered with gray radomes, and in addition deduce the electromagnetic noise:

Su-27, source
Civil aircraft radomes: Not as demanding as military radomes
Radomes for civil aircraft have been white or the color of the aircraft since a long time.
Antistatic material resisting heating is used. It can be painted in white or any color at the expense of some signal loss and boresight error, which are both acceptable for a weather radar (large targets) or ATC and satcom applications (limited path losses).