>>If gravity is from mass warping space, what’s pulling or pushing?
It's the warping of space that we feel as gravity. Jump off a cliff, and warped space created by the Earth is what we experience as an attractive force - the stretching of space/time.
>>The model doesn’t explain this. It shouldn’t matter if space is warped.
Depends on which model you mean; in the standard model, warped space does indeed determine how strong a particular point near a mass gravity would be. It's how we calculate how much mass a planet has by observing the orbital speed of it's moons.
>>An object sitting in warped space shouldn’t move either way. It’d just sit there.
No, that's not right. In warped space, there'll be an attraction toward the object warping it. With no other force holding it in place (friction, rocket engines, a rope) - it's going to begin to move toward that center of mass.
>>And if pushed, it should move either way equally. When will science just admit it’s electromagnetic attraction?
You can take a magnet and lift a nail or a pin, thereby overcoming gravitational pull of the Earth... And, we can detect the magnetic field of the Earth in different densities from it's nearly uniform gravity at a distance.