I'm skeptical about the ideological component of Soviet aid early on. Early Soviet foreign policy, particularly that of Stalin, was actually extremely pragmatic and at times arguably contrary to Soviet ideology. The early USSR actually allied with a lot of leftist nationalists: Ataturk in Turkey and Sun Yat-sen in China out of a sort of notion of "fellow travelers" and for a time actually had shockingly cordial relations with the staunchly conservative Ibn Saud. So it just goes to show that the USSR was actually quite capable of maintaining strong relations with even arch-conservative absolute monarchies like Saudi Arabia. The breakdown of Soviet-Saudi relations didn't really happen due to any particular ideological disagreements.
I feel like you're interpreting the foreign policy of the 1930's USSR with other periods of Soviet foreign policy. But it needs to be emphasised how incredibly different the 1930's USSR was from the post-WWII USSR: this isn't the communist superpower that wages an ideological war, it's an isolated regime looking to establish ties to different countries and find its place in both Europe and the world. Soviet foreign policy of this period was more focused on building new diplomatic relationships rather than promoting communist ideology.
So then what might the relations between Moscow and Addis Ababa look like ITTL?Of course, the Soviets really didn't design their foreign policy towards the former colonies, rather, the former colonies had more of a role in designing Soviet foreign policy towards them, so it's no surprise that Soviet relations in the "3rd world" didn't look like anything out of Marx or Lenin's idealized models for the world.
So then what might the relations between Moscow and Addis Ababa look like ITTL?
How plausible is it to have the Soviet Union send a Military Mission to (a Republican) Ethiopia in the late 20s to early 30s?
I doubt it would do much good. Soviet political and military tactics would only work in industrialized or semi-industrialized nations that had a modern standing army not compromised by personal military factions.
Or we could have a left-wing and nationalistic regime rise to power in Addis Ababa that attempts to actively court what it sees as a successor of the Russian Empire as well as the material and technical support it provided to Ethiopia.So likely the Soviets send a token mission either because a different faction is in the ascendant in the debates on how to spread the revolution, or because the Soviets REALLY want to stick a thumb in the eye of the Italians, or maybe some combination of both.
If the Soviet aid then plays an important role (or is seen to play an important role) in the Italo-Abyssinian war, then I can see post-war Ethiopia having a high opinion of the Soviets as the only power that cared about the Fascists before Hitler tried to burn the world down. This could have quite a few ripples on its own, as the Soviets now have even more anti-Fascist cred (and more importantly, anti-Fascist cred in the "colonial" world) and the Soviets have a real friend and positive experiences in being involved in the underdeveloped world 15 years before they forged their relationship with Nassarist Egypt. Also, a real foreign policy success in Ethiopia without regime change gives the Soviets another model for success - in OTL, the Soviets lost all their pre-war friends during WW2 or in the immediate aftermath.
On the other hand, things could start out well and relations could crash after Stalin does something like purging an ambassador that the Ethiopians like (apparently what wrecked relations with Saudi Arabia), or the Soviets could be unable to send aid of enough worth to really effect the Italo-Abyssinian war, and so there's little post war impact.
See, this is one of the parts of the scenario of this thread that interests me - the question of would Ethiopia have managed to develop her own version of Deep Operations but mainly centered around the use of huge peasant and Calvary armies? Things like this could give Ethiopia a fighting chance against the Italians if they decide to invade.Remember this is the 20s or early 30s. Yes, Soviet officers are thinking about how to apply the lessons of the civil war to mechanized warfare, but their doctrine is still based on the horse-based mobilized peasant armies of the civil war at this point.