WI, instead of invading Ethiopia from Eritrea they instead making a landing on the other shore of the Red Sea?
Cant see Great Britain being very happy about this. AFAIK GB didnt really give a damn about Ethipia due to its lack of anything useful. However, Saudi Arabia is right next door to a very large chunk of british controlled oil. The Brits would have kittens about the Italians occupying Saudi Arabia.
Cant remember whether Saudi was much of an oil producer at this stage, but if it is, then even more reason for Britain to be potentially prepared to risk war.
However, IIRC the main reason for the Italian attack was revenge for their defeat by the Ethiopians some 40 - 50 years before. What would be the POD that would make Mussolini risk war with Britain?
Besides, he had already declared himself "Protector of Islam", and don't you think that the Protector of Islam would lay claim to protect the holy places?
Would they go to war for the Saudis? I think not. Remember the British were in bed with the Hashemites in Transjordan and Iraq, and Hashemites weren't exactly friendly with the Saudis at the time. I think the British attitude to an Italian invasion of Saudi would be more like "If only they could both lose". Also I have a feeling that they'd be rather less sympathy for the Saudis that the Ethiopians in the League of Nations.
Italy was also looking for a way to connect their colonies at Eritrea and Somililand.Mussolini invaded Abyssinia because Italy had a history of intereference with that country - it was seen as being in the Italian sphere of influence, bordered as it was by Eritrea and Italian Somalialand
One of his aims was to revenge the defeat at Adowa in 1896.