If space/time is curved due to gravity then it is passive as it is being acted upon. I'd say that gravity is the cause and therefore active, but it is matter/energy that holds the cards here.
Matter/energy is the substance of all things. Time and space only exist in the attempt to rationalize our perceptions and limitations.
You have that backwards. Gravity is due to space-time curvature. The curvature of space-time might be due to mass, but the force of gravity is itself the "active" component of space-time curvature. This is why gravity curves the path of light when light has no mass for the gravity to act upon.