Tested with an exaggerated version of Xilefian's BlusteryDay resource pack. Exaggerated version is attached as BlusteryDay_Exaggerated.zip. Main changes are the amplitude of the position offset vector is multiplied by a factor of 100.

Due to file size limits, here is a recorded version of the bug as an unlisted YouTube video. The bug is most prominent along the X-Z diagonal when both coordinates are either positive or negative at once.