The separation of Church and state is a declaration of the state. In France, the state declared it in order to protect the Church from influence of the state. In the Philippines it was being invoked in order to pursue immorality by the state, among others.
As far as I know, like others who posted, that declaration is not part of the teachings of the Church. Since it the state who declares it, the state must be in the forefront of implementing it, that is, the state must refrain from pretending to do what is good for the people to the point of leading the people away from God by encouraging them to go away from moral practices as taught by the Church.
The homily of a priest in the Cathedral of Baguio, few months past, about the Reproductive Health Bill was laudable. That was courageously stating the guidelines for the Catholic population, lawmakers included, in opposing possible passage into law of a measure that runs counter to morality. That priest cannot logically be considered as violating separating of Church and state. He was performing his duty to educate those who can hear him regarding morality. What he did was protected by the freedom of religion guaranteed by the constitution.