That is why physics was invented :).
Lets take it a step at a time:
Let's say I'm in a space station, hurtling towards our galaxy nearly close to the speed of light. From my reference frame, I see the galaxy coming towards my ship at the same speed.
Fair enough. True also in Newtonian mechanics, there is no acceleration and it is just a matter of coordinate choice for the rest frame. There is no cause and effect.
I pass the Sun, and am affected by its gravity.
Now acceleration is introduced, and this means there is a central force as far as Newtonian mechanics goes. For General Relativity, the space is distorted and the space station follows the geodesic. The cause of the change is the force/geodesic.
From Earth's point of view, the gravity of the sun deflected my spaceship's trajectory. From my point of view in the spaceship, the trajectory of the entire galaxy changed very rapidly.
From my reference frame, how did my space station cause an entire galaxy to change course?
That is why we have developed physics. The coordinate system change one makes by "earth's pov" and "my pov" is not causal. The cause of the changes comes from the forces in the system or in GR the space distortion the Sun's gravitational field causes in its area of measurable influence. How the coordinate system is described mathematically is only a matter of convenience. You could take the pov of an ant moving on the earth. You would need complicated geometric calculations to see why the spaceship is changing rapidly while going for food, but the relation is mathematical, not causal.
The epicycle geocentric view comes to mind. It is a correct mathematically coordinate system but has little correlation with the forces that become apparent in the heliocentric system. So your pov is a spaceship-centric pov.