Evey time I squat my hips get super stiff... I think to protect my lower back, which always hurts to some degree.
I haven't found any mobility drills or stretching that consistently loosens them up and gives me enough ROM. Running for about 45 minutes works the best, but it's hard to do skill work after that...
I've been backing off for years now, but still look for some way to keep squatting.
Eating less vegetables and more meat also definitely helped. I think low-calorie foods and vegetables in particular were bloating my abdomen and pushing my hips out of position.