Its unlikely. Ethiopia isn't the only Christian part of Africa: the region around modern Eritrea, north of Ethiopia, was also heavily Christian when it was colonised by the Italians in 1882, South Sudan likely had many large Christian communities when it was colonised by the British around the end of the 19th century and of course the Boers weren't spared destruction at the hands of the Cape Colony despite their protestant faith and European origins.

Its also important to note that just because Ethiopia didn't end up under colonial rule by the conclusion of the partitions, that doesn't mean they didn't try! Italy invaded Ethiopia in 1895, around the same time the rest of the European powers were building their own colonial empires in Africa (Great Britain had consolidated her holdings in South Africa in a series of wars between 1879 and 1902 and then began her expansion in East Africa in the 1890s. So Italy wasn't very far behind at all in her invasion!)

However, the invasion was a shambles and the Ethiopian forces (Thanks somewhat to arms and aid from Russia, France and the UK) overwhelmed a small Italian garrisson in an unfinished fort in Meqele, scaring the tiny Italian force which had been sent to subdue the uncowed Ethiopians. The Italians had massively underestimated the Ethiopians mostly out of racism, an easy mistake to make at the time since the rest of the African peoples subdued over the previous decade or so had been mostly unorganised tribes and even hunter-gatherers, whereas Ethiopia had been an established state for over a millenium at this point. The Italian generals were anxious, rightly, about the size of their force but the Italian leadership in Rome, blinded by racial supremacy, refused to be cowed by blacks and ordered the Italian generals to suck it up and meet the Ethiopians in the field to prove to the world that a bunch of savages were no match for the well-drilled Italian army and avenge the defeat of the Italian garrisson at Meqele earlier.

The Generals, however, had been right to be anxious and were smashed by the far larger Ethiopian force at Adwa in March 1896 - despite expecting spear-armed savages, the 17,000 or so Italians were met with an Ethiopian army numbering up to 120,000 men, which had been granted 100,000 rifles (Many of which were state of the art, fresh from Italy's troublesome colonial rivals) and 50 artillery pieces resulting in a humiliating and costly slaughter for the Italians, 7000 men, almost half the Italian force, were killed in just one day. Overall the campaign cost the lives of 15,000 Italians and huge sums of money dissuading any future attempts at colonising Ethiopia. The other powers were not only pleased that their rival, Italy, had been trounced in the field but were also wary of the power Ethiopia had been able to bring to bear during the war, so drew up treaties to formally recognise Ethiopia as a state. After this there were no real attempts to colonise her until Mussolini tried again in 1936, by which time Ethiopia had her own seat in the League of Nations and her takeover outraged leaders around the world - quite the step up from the backwards savages the Italians had thought they were dealing with!

TL;DR Ethiopia wasn't initially given much extra respect despite her Christian status but was, through a combination of good terrain and Italian stupidity, able to actually beat her colonisers, thus securing her independence in a way no other African state could.

There is an angle to this that does involves Christianity. A lot of 19th century European colonialism involved rhetoric about Christianizing the colonial non-Christians. Christianity went hand-in-hand with the "civilizing" mission of European colonial powers: Christianity was an important aspect of the brand of European civilization that these colonial powers were bringing to Africa and other parts of the world.

That said, European intellectuals were pretty quick to denigrate Ethiopian Christianity as a lesser or primitive form of Christianity, stuck in biblical times and tainted by the Islamic and Pagan traditions surrounding the nation.

Just as one example, the British archaeologist Theodore Bent wrote a book in 1893 called The Sacred City of the Ethiopians: Being a Record of Travel and Research in Abyssinia in 1893. Mostly covering the archaeological site of the city of Aksum (and related archaeological findings), the book also made commentary on the character of Ethiopian culture.

In the preface of the book he mentions that the text will give “…special attention to the religious observances of the primitive church…”(Bent 1896: viii). This is a theme that repeats throughout the book and other British work on Ethiopia, emphasizing the "primitive" or "Bibilical" nature of Ethiopian Christianity as compared to more modern, European-style Christianity. Indeed, the claims of the Solomonid emperors of Ethiopia to be descended from King Solomon by way of the Queen of Sheba was turned around and used as evidence of the comparative 'primitiveness' of Ethiopian Christianity.

In the forward to the 1896 edition of Bent's book (being written after the failed Italian invasion in 1985) he writes that:“…all must recognize that theirs [the Italian’s] is the cause of civilisation and humanity in the future development of this corner of the Dark Continent” (Bent 1896: vi). There is clearly a sentiment that despite their Christian monarch, Ethiopia is no different than any other nation in Africa.

On the other hand, when the Ethiopian emperor Hailie Selassie traveled to Geneva in 1936 to make an appeal to the League of Nations to intervene in the second Italian invasion of his country, he purposefully made a stop in Jerusalem and several of its holy sites to underscore his status as a Christian monarch. In his speech to the League of Nations, he specifically incorporates Christian imagery and verbiage in order to underscore Ethiopian status as a Christian nation. To quote (emphasis my own): "Apart from the Kingdom of the Lord there is not on this earth any nation that is superior to any other. Should it happen that a strong Government finds it may with impunity destroy a weak people, then the hour strikes for that weak people to appeal to the League of Nations to give its judgment in all freedom. God and history will remember your judgment." It seems he was aware of the place Christianity had in the ideology behind European colonialism and tried to use that to his advantage in global politics.

Sources: Bent, J. Theodore 1896 The Sacred City of the Ethiopians: Being a Record of Travel and Research in Abyssinia in 1893. London: Longmans, Green and Co., New Edition.

There was an attempt to conquer (and presumably colonize) Ethiopia way back in 1529, when the Somali Imam, Ahmed Gargn, supported by an Ottoman legion invaded Ethiopia.

This invasion came very close to success. Fortunately for the Ethiopians, the Portuguese had arrived in the Indian Ocean, and Christovao DaGama (second son of Vasco DaGama) led a Portuguese expedition of 400 musketeers, some cavalry, and a few other troops to the aid of their fellow Christians in Ethiopia.

The war went on until 1557. The Portuguese were instrumental in winning several critical battles. Christovao was killed after losing another battle against the Muslims, but his soldiers fought on and were key to defeating the attempt to conquering Ethiopia.

So, Ethiopia would have been conquered and colonized by the Muslim powers if not for Portuguese support. That support was only provided because the Portuguese saw the Ethiopians as fellow Christians.

So, Yes, Ethiopia was not colonized (back in the 16th century) due to the prevalence of Christianity.