I’m running the bed that came with my Ender 3 pro (using a pei sheet, this is repeatable with glass too), been having this issue for a while I think. Is it time to replace the bed?
Update: Figured it out, what my bl touch was attached to was very loose, and was going up on the far side of the x gantry. and it’s now fine.
Make sure there isn’t too much tension on the cables to the hotend assembly. Could be pulling too tight and lifting a bit when it gets too the far side
This is the right answer. You’re hot end is pulling tight and causing this skew.