What is the explanation of the color similarity that the majority of natural satellites obtain?
The colour of a natural satellite is almost entirely based off the atmosphere and surface of the satellite. The moon Io, of Jupiter is not grey and is coloured because of sulfur on its surface that create a colour. Io has a very thin atmosphere.
So that brings us to your question, why is the majority of natural satellites grey? We know that moon's colours are dependent on what they are made up of and if they have an atmosphere, so the basic answer is that the majority of moons are grey because they do not hold an atmosphere, and are made up of rock. Our moon is made out of basalts which are a grey rock. You can probably go out and research what certain moons are made of, and find out more about the rocks on them and how they affect the colour of the planet.