You have a "Tight Psoas" on the right side.
I'm no expert, but your Psoas is a "deep postural" muscle that connects your spine to your thigh, like "under" your abs.
When it cranks down, it pulls your ribs towards your knee. This can make your butt stick out. If one side (your right side) is tighter than the other side, it can make your pelvis "twist." In this position, your glute/hip/abs/obliques/adductors/abductors all start to work in a "dysfunctional" way.
After awhile, you kind of "train" yourself to go into this dysfunctional "movement pattern."
After you do your self myofacial release, try to hip hikes, clam shells and seated Psoas holds. They are like easier moves, or a regression of the glute thrust move.
As far as a Root Cause, different experts will say different things.
I would start by checking out your feet and ankles. Do you have a flat foot or collapsed arch on the "bad side."