Al Islam ya'lu la yu'la alaihi: 'Islam is the greatest and will not accept superiority of a non-Muslim person' is some kind of Qaidah Fiqh, a basic idea in Islamic thinking. It can be explained in very different ways. One is, that God has created human beings different: men and women, various nations and tribes (Qur'an: 49:13) and also of different religions and denominations: so, faqtabiqu bi'l khairat, we have to struggle to be the best. There is also a more restricted explanation, that Muslims should be ruled by Muslims only, not by other people.
A tricky verse of the Qur'an (5:51) forbids the Believers to take Jews and Christians as 'partners, friends, awliya' 'He among you who taketh them for friends is one of them.'
This is extended in many ways: if you are dressed like them, 'you are one of them', ... if you join their festivals, like the yaum al hubb or Valentine's Day: you are one of them. This was a fatwa that I used at the University College, to explain the structure and logic of a fatwa and how it is used to solve modern questions.
On 27 September 2016 the Chinese Christian Ahok, governor of Jakarta visited the islands in the bay of Jakarta, Pulau Seribu and quoted this verse, because the population of the islands is strongly Muslim and Ahok has been educated in a state school where Islam was thoroughly instructed. The verse 5:51 can be explained in various ways too. Ahok wanted to state that he is a friend for Muslims, who also gave good subsidies and donations to Muslim schools, madrasah. There are new elections for local officials in 2017 coming and popularity is important and religion is again an issue. Ahok took the wrong verse or Muslims took different interpretations and Ahok was corrected and criticised by the local Muslim Council. He apologised at various occasions.
But one day later (22 October 2016) the Jakarta Post mentioned that a number of NU activists praised Ahok (Basuki Tjahaja) for his concern to understand and deal with Muslims.