By the time of the invasion they only had Russian backing due to the Orthodox Christian ties. Britain and France both wanted Ethiopia and Menelik used that to his advantage, but at the same time these so called allies didn't allow Ethiopia to join in the industrial age because it was a Black country. But no lies, without the Russians weapons and some of the training they provided my name would probably be Angelo and I'd be way more light skinned.
But terrain and the sheer numbers also made conquering Ethiopia a very difficult task in those days. There were far too many advantages the Ethiopians had that others didn't on the continent.
No, Italy didn't colonize Ethiopia. It was an occupation, the Italians only controlled the urban centered but had no control of the rural/remote parts of the country. The Italians were hemorraging money throughout the years they were in Ethiopia which partly aided in their rapid decline throughout WWII. Eritrea was a part of the country that was disputed by many nations including Ethiopia, but in truth the country was sold off by Menelik to Italy in order to weaken the Yohannes IV's true heir Ras Mengesha whose domain included the region which became Eritrea. So that forfeiture makes your point of being partly-colonized invalid.
Emotionally I agree with you, allowing the land that became Eritrea to be colonized was like Ethiopia was already colonized. But that's emotion, not fact. Aside from that, I'm not sure about the white colonizers being helped by Ethiopians bit. At most, the Brits and Ethis collaborated against the Somali people but that's after the Ethiopians/Somali developed a long and bitter rivalry against one another so for Menelik it was inconsequential. It's easy for us to sit here in 2017 and wag our fingers but at that time the game for Ethiopia's leaders was to keep the Europeans at bay while stocking up on weapons and building alliances with other countries that could ensure their sovereignty. For a Black leader to have done that in the 19th century is impressive in spite the mistakes that's why other Africans and African descended people "put Ethiopia on a pedastal".
Black people throughout the Diaspora were very involved actually. There were race riots in Harlem with Black folks beating down Italians over the invasion. It also inspired some of the brightest minds in the Black world to provide their efforts to the liberation of Ethiopia. A lot of great literature came out of this time, in fact a long lost Claude McKay novel (Harlem Renaissance author, I believe he's of Jamaican descent) was just released a few weeks ago which describes what Harlem was like during the Italio-Ethiopian War.
Aside from that the other poster is right. The Great Depression made the LON countries look more inward to their own people/problems. Italy's successful invasion and occupation was the fire that lit the fuse to WWII because it showed that the LON was completely impotent against any threats and that even if the Brits or French wanted to jump out there they couldn't because they weren't as invested in military as the Italians, Germans, and Japanese had become by that point.
When you think about it, the Axis Powers came pretty close to controlling nearly the whole Nile Valley and Northeast Coast of Africa. If Italy/Germany has the same success in Libya and Egypt that they had against Europe only Sudan and Somaliland would've been left in that region in terms of Allied influence/control. Would've been brutal for the Allied effort in Europe.