Is secularism compatible with Islam?

If secularism is defined as a set of political ideas aiming to separate the governance of state from religion (short version), is secularism compatible with Islam? By that, I mean, can Muslims legally (with respect to Islam, not the state) be supportive of the separation of Islam and state and supportive of a state model founded on religiously neutral principles of rational [scientific and materialistic (in a philosophical, not consumerist sense)] social science and morality?