Are Muslims Young Earth Creationists?
This question is irrelevant to Muslims and usually it's not even raised. We believe the entire universe is created by God. As for how and when, this is left for our observations and examinations i.e. this is a question of science. And we are ordered in the Qur'an to study the creation of God and understand how they are created. But in any case, God is the first cause.
To be a Muslim, does one have to disbelieve in evolution?
The previous reply is relevant to this question too. Evolution or not is a question left for science. Evolution or not...in any case, Allah is the first cause, the planner and the sustainer.
But the Qur'an clearly states that Adam was created directly. And it seems the creation of Adam was a specific case like the creation of Jesus. Science says that the human offspring is the result of the meeting of an ovum and a sperm. But when we believe that Jesus was created without a father, it doesn't mean it contradicts science. But it means that the difference between the believer and the disbeliever that the believer believes who created the mechanism of the ovum and sperm meeting to give a zygote to give a human being is God and He is able to change this mechanism whenever He wills and this is what we call "miracle". The Creator of the observed governing laws, can change them whenever He wants. God doesn't need certain mechanisms to create, Allah only says be and it is.
"The similitude of Jesus before Allah is as that of Adam; He created him from dust, then said to him: "Be". And he was." Holy Qur'an, Ali-Imran: 59
The miraculous exceptional event is not subjected to the question of science. The miracle is a thing and our knowledge based on our scientific observation and measure is a completely different thing.
What I am saying that the direct creation of Adam could be a specific case just like it was with Jesus.
And
what is for sure that the creation of Adam as it's mentioned in the Qur'an doesn't contradict with the findings, on the contrary, for example: human beings are genetically highly homogeneous compared to the other species which says that we originated from a small population. No contradiction.
Is the Qu'ran consistent with science?
Yes.