Like Shangalar says, green dogs are friendly to players. They will defend players and other friendly critters from attacks from any neutral or hostile critters. They will not interfere with PvP.
In fact critters you meet in random encounters and in the core may have one of four different "hostility levels":
Hostile - attacks everything in sight, including other hostile critters.
Neutral - attacks hostile critters and anybody or anything that attacks them first.
Friendly - attacks hostile critters and defends friendly critters and any players from attacks from anything that is neutral or hostile.
Allied - pretty much like guards are supposed to work - they owe allegience to one of the factions, and as such will defend anyone in that faction from anything except others in the same faction. They will also attack the intimate enemy of their faction. Shooting them will reduce your reputation with that faction.
So far no allied critters have been implemented, but it might be possible in the future, especially in the gate maps or in zones controlled by some faction.
As you've already discovered, dogs come in both hostile, neutral and friendly groups, and you can separate them by the colour of their contour.