I replaced my iPhone 6s screen a couple of months ago with one supplied by ifixit. I’ve had intermittent shaky icons since and today the screen rotate no longer works. I’m not that impressed with the new screen (colours and brightness didn’t seem accurate, and I’ve had to turn off the 3D Touch because the screen sensitivity is rubbish). As I said, it’s been 2 months since the repair with no obvious issues besides these occasional shaking episodes, so I can’t even say if the two are related.
Amendment: The wood screw suggestion does not work for all models (I have just broken a couple of rubber boots removing them) - this was because they had a hard plastic center that prevented me screwing in a wood screw to aid removal and forcing me to try and pull them out by hand.