The main roles in the government of Lebanon are split among Sunni Muslims, Shia Muslims and Christians. The president is Christian. The prime minister and speaker of parliament are muslim (one Shia and the other Sunni).
I am not saying this was a good system - quite obviously it has not worked well. But to blame all of this on Muslims is nonsense.
Also important: some features of Lebanese government are invariant to demographic changes bc the government has declined to conduct a new census.
For reference: https://en.m.wikipedia.org/wiki/Politics_of_Lebanon