What is the ruling of the religion on engagement before marriage with the knowledge and consent of both parents?

If the pre-marital relationship means there is a connection between two non-mahrams through speech without necessity, or correspondence, or meeting, and so on, then it is not permissible in Sharia, even if the family knows about it and consents to it. It is not permissible to act upon any fatwas that might permit such relationships, and one's heart should not be consulted when committing acts of disobedience.