Re: Safety question: Loose primer pockets in new brass.
Yes. It should cause you to take a hard look at that brass and those primers. If they are vibrating in a plastic ammo box on a washboard road they may back out. If they are in a rifle magazine on the same road, they can still back out and cause feeding problems and chambering problems and possibly leakers on firing?
When I get a loose primer "feel", I toss the case. Don't attempt to salvage the primer. But, you say this is new brass? That's unusual. And, you didn't "uniform" the primer pockets, right?
If you have other brand primers, I'd try seating them, just to see.
Other than that, sounds like you may have a bad lot, most likely, the brass?
Good hunting. LB