How to do barbell shrugs?

Today, I encountered an unexpected anatomical hazard while attempting barbell shrugs. Normally, I stick to a hex bar or dumbbells, but since the gym was packed, I had to settle for a regular barbell. Big mistake.

First rep in, my trouser snake got way too familiar with the bar. It felt like I was foam rolling the worst possible muscle group. No matter what I did, wider stance, strategic tucking, hips back, nothing helped, I was in pain and quit.

Do I need to wear a fucking cup? Am I doing it wrong? Any advice is welcome.