The geographic North Pole isn’t moving on the earth. The magnetic north is shifting, NOT the rotational axis.
The sun is a sphere that puts off relatively constant radiation, so if for some reason it’s rotational axis is shifting, I don’t know that it would change weather. But you have to ask yourself the question... what would make an entire planet or sun or moon’s rotational axis shift? Something would have to push or pull on it to have this effect. You would need to find whatever this is. If it’s powerful enough to disturb the movement of the sun then it would be enormous.
I think you need to learn the basics.