I didn’t see anywhere that neutrals cannot invade other neutrals. If that is the case I would think that Russia could not invade the middle east, as the alpha 2 rules state:
3. If the Soviet Union is at war with Axis powers on only one map, it is still under the restrictions of being a neutral power. In other words, war with Japan lifts those restrictions from the USSR on the Pacific map only, and war with Germany and/or Italy lifts those restrictions on the Europe map only.
I did find that combat moves are labelled “at war powers only” so it would seem that you cannot invade a pro Axis nuetral as Russia, since that would be a combat moves. I gues it would make sense that they cannot move into a pro allies neutral as they are not yet an ally.